Tips To Remember How Math Logarithmic Notation Works

Logarithms are really fun and interesting, but I have seen many students find changing logarithmic notation to exponential notation and vice versa quite confusing. Well here are some useful tips to make you remember that this conversion is simpler than you have expected.

The exponential form is where we have the base number multiplied according the exponent to get the answer. Here is an example from online math tutor:

When you multiply 2 four times you get 16. That is 2 x 2 x 2 x 2 = 16.

This can be written in the exponential form as 24 = 16. Let’s look deeper into this notation:


Let’s now try to follow how we can convert the exponential notation to the logarithmic notation:


As show above, both the exponential notation and the logarithmic notation have the same base number. Next, there is an exchange in the exponent and answer while writing it in the logarithmic notation.

This can be better understood with an example:

Convert 34 = 81 from an exponential notation to logarithmic notation.

Here 3 is the base number which will remain the same even in the logarithmic form.

We have 4 as the exponent and 81is the answer which can be written as:


Did you get a little hold of this method? Good let me show you one more example:

Convert 52 = 25 from exponential form to logarithmic form.

Everyone likes the 5 times table, for some reason it’s quite easy to memorize.

Here observe 5 is the base number and 2 happens to be the exponent. Multiplying 5 x 5 gives 25 as the answer. Now converting the exponential form to logarithmic form:


Taking a step further, let us now convert the logarithmic notation into exponential notation applying the same process backwards.

Convert log4 64 = 3 from logarithmic notation to exponential notation.

Here the given logarithmic notation can be changed to exponential notation by keeping the base number 4 the same. Follow the steps below:


Hence the exponential notation for the given question is 43 = 64.

Good so far! Now, have you ever observed some logarithms written without a base?

For example, notations like log 5, log 16 or log 150. Are they really without any base number? The answer is NO! They have a base number which is 10 it’s called the common base.

Hence, logarithms with base number 10 are called common logarithms. This can be shown as below:


Convert the given exponential form 103 = 1000 to logarithmic form?

Here we have the base number for the exponential form as 10, so the final answer will be a common logarithm. Hence we can write the given question into a logarithmic notation as follows:


So the final answer is log (1000) = 3. [Not to forget it still has a base 10.]

Now you are familiar with the logarithmic notation and ready to change exponential notation into logarithmic notation. But remember logarithms does not stop here, these are just few useful tips to get you started with the logarithmic notation.

Read more – Solving Logarithmic Equations

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How to Solve Algebra Word Problems in 5 Steps

For solving Algebra word problems you need to use your logic and find out answers for the problem. Here are 5 steps that help you solve Algebra problems with ease

  1. Identify the problem
  2. Identify what you know
  3. Make a plan
  4. Carry out the plan
  5. Verify whether your answer makes sense

Step 1

Identify the problem

The steps for identifying the problem are

  • Express the problem question or statement.
  • Identify the unit of the final answer.
  • Express the problem question or statement.

You find Algebra word problems in the form of a question or statement.


Question How many saplings Brown needs to plant? How many televisions Brenda needs to sell to earn $20000?

Statement Find the number of saplings Brown has to plant. Solve for the number of televisions Brenda has to sell to earn $20000.

  • Identify the final unit of the answer

After understanding the purpose of the word problem, try to find out in what unit the answer will be like miles, ounces, pesos, number of trees or number of televisions.

Example for step1

Christiana is making brownies to serve at the family picnic. If the recipe calls for 21/2 cups of cocoa to serve 4 people, how many cups will she need for 60 people who attend the picnic?

  • Identify the problem: how many cups Christiana needs if 60 people attend the picnic?
  • Identify the final unit of answer: Cups

 Step 2

Identify what you know

I need more information What information you have is not adequate and you need more information.

Example for step 2 

Sarah is carpeting a rectangular room in her house. The length of the room is(x+2) feet and the breadth of the room is (x-6) feet and the area of the room is 84 square feet. Find the length and width of the room. Identify what you know

  • Sarah is carpeting a rectangular room
  • The length of the room is x+2
  • The breadth of the room is x-6
  • The area of the room is 84 square feet.
  • The formula for the area of a rectangle is A=lw
  • I need to find x to find the length and breadth of the room.

Step 3

Make a plan

Methods of building your plan

  • Write down your plan
  • Talk about your plan
  • Make a table
  • Draw a bar graph, line or circle
  • Draw any other type of graph
  • Draw a picture

Example for step 3

The Damsels Theater expects 275 patrons every weekend per new movie. How many new movies they will show if they expect 2200 patrons this week end?

  • For every new movie, 275 patrons come to Damsels Theater
  • 1 movie     =275 patrons
  • 2movies =275*2=550 patrons
  • 3 movies=275*3=825 patrons
  • 275*number of movies=2200 or 275*m=2200(m represents the number of movies)
  • Solve for m to find the answer

Step 4

Carry out the plan

Verify whether the plan is sensible. Check whether you have not missed anything or did not approach the problem in the wrong manner.

Example for step 4

Ben and Jack run a combined distance of 28 miles. Ben runs three times as many miles as Jack. How many miles does Jack run?

The plan

  • B+J=28 where B represents the number of miles run by Ben and J represents the miles run by Jack.
  • B=3*J because Ben runs three times as many miles as Jack.
  • Replace B with 3*J in the equation B+J=28

Carry out the plan

  • 3*J+J=28
  • 4*J=28
  • Solve for J: J=7

Step 5

Verify whether your answer makes sense

In the last step you have two red flags that signal wrong answers

  • Your answer is too big or too small
  • The question remains unanswered

Example for step 5

John is driving from his house to his company. On Monday morning John drives 6 miles north on Peter’s road. Then he drives 8 miles east on Willie’s Road to reach his company. On Tuesday morning, John avoids Peter’s and Willie’s Roads. What is the difference between the number of miles John drives on Monday and Tuesday mornings?

John’s drive to his company resembles a right triangle. You can use Pythagorean Theorem.geometry10 miles is the answer

Verify whether your answer makes sense

No. The answer is the direct distance between John’s company and house. It is not the answer for the question what is the difference between the number of miles John drives on Monday and Tues day mornings?

Make a new plan

  • Find the direct distance
  • Add 6 miles and 8 miles to find the total distance traveled on Peter’s and Willie’s Roads
  • Find the difference between the numbers in steps 1 and 2
  • Distance between the company and house is 10 miles
  • Distance traveled on Peter’s and Willie’s Roads is 6+8=14miles
  • Difference between the numbers 14-10= 4 miles

The answer is correct as per arithmetic and it makes sense.

Doing Algebra word problems through step by step approach is logical easy and fun.


How Online Math Tutoring Helps Students To Solve College Math Problems Easily

A large number of students are restoring towards college programs, yet just one-third of them will graduate with degrees. Naturally, there are so many reasons for high dropout rates, however, some reports show that the students struggle with math course, which is a big intruder.

Prior to registering for classes, most colleges need that students take at least three placement tests. These placement tests include a fundamental math section, a reading comprehension section & a writing competition section.

Approximately half of potential college students struggle with math tests, and hence, need college math help. Even at colleges or community colleges, most degrees call for the successful completion of different college math problems, and many students continuously struggle to get out of it.

Apparently, lowering the college dropout rate proves to be a turning point on preparing students for college level math.

Math tests- How Students can improve their Score?

Scoring well on the math tests can save students’ a lot of time, effort as well as money in long run. In many cases, counteractive college level math classes do not count towards degree needs, and hence, scoring on tests can save students’ tuition fees to a greater extent. The best way to prepare for the test is to get the challenging matter working again, particularly if a lot of time has wasted since the last math class.

A number of cost-effective options are out there that can help, online math tutor is full of knowledge-base and samples on basic algebra, geometry, and almost every math-related problem. Students can garner the benefits of online math help through personal online tutoring classes.

Learning, being repeated of forgotten math concepts, just staring math right on the face again boosts the confidence level, enhances proficiency and improves scores on tests.

Read more – Top 10 Tips To Help With Math Homework

Remedial Online College Math Help Classes:

Most online tutoring classes for math boast an open-door policy that means students will not be refused admissions considering their poor test scores. Most of these college math help classes are populated with non-traditional students, many of whom study, work or raise a family simultaneously. In online tutoring for math, the tutor provides individual attention and help with various math problems students encounter these days, at an easy pace that lets students to really grasp whatever they are learning. Here, students have plenty of opportunities to practice every concept they learn under the guidance of an individual, expert tutor.

The students, who do relish success in remedial classes, attribute their brand new understanding to good teaching practices. The online math tutor breaks down every problem into a sequential small steps that traditional class teacher systematically fail to do.

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Areas of Math, College Students Struggle With

Probability and Statistics:

Many learners struggle in Probability & Statistics, although it’s not their fault. After all, these subjects have their own unique language as well as a set of rules. However, the frustration encountered by the students in this area can downgrade their self-confidence.

If the student is having a problem in Probability & Statistics, look for a broad, step-by-step tutorial, an approach which simplifies complex concepts by splitting them into small steps, via illustrations & facilitating real-life examples.


Those who need help with calculus need not to be fret upon as online help for college level math tackles this too. Calculus is perhaps one of the most difficult subjects for students, even for high achievers. But, online math tutor helps students master this subject with ease.

This is based on a special type of logic- once a student gets familiar with it; it becomes easy to resolve any type of problem. But, the problem is not all students are equal or fast learners. Some students are slow learners and they learn best at different paces & in different environments as compared to others.


Geometry is a subject that many students dread with. The shapes of geometry don’t translate very well on a board, students call for a much more visual imagination to grasp the concept like angles, lines, points, analytical geometry, parallel lines, the coordinate plane, midpoints, distance, congruent triangles, slopes, deduction & formal proofs, equation of lines, introduction of triangles, polygons, right triangles Pythagorean theorem, angles of triangles, similar triangles, congruent triangles, quadrilaterals: rectangles, trapezoids, rhombuses, parallelograms, squares; perimeters & areas circles; lines associated with circles: chord, diameter, radius, tangent, secant; the equation of a circle; angles related to a circle; area & circumference! On the other hand, geometry is a necessary component of a better education.

Online math help tutorials and tutors can help students learn complex mathematical concepts easily. Students need to find a math tutor who can is well-versed and can offer a comprehensive tutorial program & help students grasp challenging concepts through repetition. Online tutors provide hundreds of interactive exercises to ensure that the students master all the formulas, as well as concepts. The can also assist with suggesting and providing good math books.

Read more – Some Important Advantages Of Online Math Tutor 

The knowledge & sense of achievement online math tutoring can bring to the students will play a big role in shaping the future of the students. Not only it helps student clear their concepts, but also help them earn good grades in college.

Get round the clock and expert math help online -at Tutor Pace

math helpMath, being an important subject needs constant practice of problems. Students, due to lack of time to practice more number of questions face innumerable issues with handling them at last minute. Hence, to enhance the math learning, it is essential to enroll in online math tutoring where students are provided with the flexibility to select their time and place of study.

Tutors help students with diverse topics in math, including algebra, pre-calculus, geometry and much more. Tutors don’t spoon feed students with solutions instead help them grasp fundamentals and then move to advance concepts. The math tutoring is offered round the clock. You can personalize your math schedules and learning time as per your convenience. There is always a math tutor available for you whenever you face problems with solving questions or understanding some concept.

Math tutoring for different assignments

Math tutors at Tutor Expert undergo a series of qualifying tests and possess the expertise to interact with the students. They make students learn basics and even master difficult concepts. Math tutors help students with-

  • Completing math homework properly
  • Assignments and worksheets
  • Preparing for math tests
  • Studying for college exams
  • Cross checking solutions

Enroll in math help at Tutor Pace and improve your scores today. You can tailor your schedules yourself, log into your account anytime and anywhere and find best tutor to assist you. Master Math and get an upper edge in class than your peers with our expert math tutoring.

Find Online Tutoring at Affordable Rates to Enhance Your Learning Abilities!

Online Tutoring Anything affordable and free suits modern life rolled up by heavy expenditures for anything and everything on earth. That too, education has become highly expensive and you can’t help it. Suppose you find some freebies one way or the other, you sigh with relief and start learning with a new inspiration.  A welcoming sign for the parents too who search a way out to cut short the expenses for their kids’ education.

Ways to find online tutoring at affordable rates

  • There are study programs at affordable rates which you could try for your better knowledge in subjects. This you  could do through seeking  tutoring for specific topics
  • You could go in for tutoring programs  for a restricted time like twice a week
  • You could sit for free diagnosis test and choose programs according to your abilities-whether you need prolonged tutoring programs or  limited live chat help  for a few  homework topics

There are many online tutoring services which provide you free services to promote the purpose of education. You could make use of them. This especially comes true for your Math help which you need many a time when you sit with your homework in Algebra or Calculus. Once you have the rudimentary Math skills in specific branches of Math, seeking help for some time to fill in the gaps in your learning process or to gain extra edge in your knowledge gathering helps you  increase your efficiency in Math doing. Math online free tutoring is of much use to you in this regard.

You could contact Tutor Pace to gain good packages of tutoring at affordable rates for all subjects.

Math Tutors- Some Big Things They Do for You

Math Tutors

Math is a labyrinth which makes no way out for you once you are caught up in its mess.  You have to fight out the demon in its regime- what to do and how to solve?  Tutor Pace comes before you with its Math tutors who relax all the tightening grip of Math concepts on you and relieve you of your homework burden.

Some big things done by our Math tutors for you!

Not that you enter a merry land, when you usher in the threshold of any Math tutoring. There are signals of miscommunication and misunderstanding between you and your tutors. Our tutors do not give you that trouble; they start their sessions with a diagnostic test and demos and thus catch your pulse to know what actually torments you – lack of conceptual understanding or basics or prejudices against the subject or incomplete knowledge in the previous grades. They start their tutoring accordingly and make you realize the fact that Math is easy to catch, once you know the trick to approach it.

Algebra, Calculus or Geometry- the problem is to find out what actually is the trouble shooting area and how to rectify. You cannot sit on previous year’s grades which could be your best. The new grade   with different topics, say as in Algebra, would be daunting and you feel shrunken and withdrawn to self, starting to skip your Math classes. In such circumstances, it is only our tutors who prove a boon to you with their customized approaches and excellent remedies.

Connect to us to do your Math with confidence and courage.

Math help required? Make it more interesting with online math tutor!

online tutoring for Trigonometry

Mathematics is a tough subject. even if you are a math genius or a math fan, there might be times when you’d require math help for, say, algebra homework, geometry homework and more. Study the tough algebraic concepts of monomials, binomials, polynomials, exponential patterns, intercepts, graphs, quad equations, variables and more. Now you can study all this at one stop with the help of online math tutor and get the most effective and instant math help.

There would many students who’d be wondering why go for online math help and assign an online math tutor? Well, here is the answer to all your queries.

  • With online math help you can complete algebra homework in a jiffy
  • You are well prepared for your future tests
  • You are up to date with the curriculum going on in the class
  • You’re on time homework submission increases your class assessment
  • And over all, studying with online math tutor is:
    • More interesting
    • More fun
    • Saves your travel time to other tuitions
    • Gives you a personalized review of your mistakes or points
    • Clears your doubts easily

Apart from this, the services these tutors provide are customized as per each child and are in easy reach while being light on your expenses too.

With math help from online math tutor you not just get algebra homework help you are taking your studies to a next level.

Excel in Math…Interactive Learning Sessions!

Internet math tutoring sessions are fun and interactive; unlike classroom activities. Online interactive sessions help you to reach your potential faster. Sharing of whiteboard, the advantage of face to face discussion from the comfort of home makes learning interesting. Internet learning is a technology that provides the convenience of learning at your own place, time and pace.

Benefits of Math Online Tutoring:

  • One-on-one live session with an expert teacher
  • Instant Assignment help
  • Fully interactive discussion using voice, chat and whiteboard
  • Schedule your tutor at a convenient time for you
  • All lessons are recorded and available for review
  • Have a personal online tutor to help you score your expected grades
  • Use of advanced technology that makes learning easy and fun

Tutor Pace, an e-learning website providing an effective online math tutoring session to help your child to understand and master the concepts of numbers. Our online math tutors with deep knowledge and understanding of mathematics are available 24*7. Our training methods are designed in a way so that students progress to higher levels of mathematics easily.

Need Help With Math Questions? You’ve Found The Right Place!

Much of your achievement or failure in math can be laid at the feet of your study habits. Do you follow a good math study habit? Take this survey and find out.

What is your approach to math?  Tutor Paces’ math sessions are planned considering the different understanding style of the students. These sessions emphasize the practicalities rather than on the mechanisms. The online tutoring website is a dependable platform demonstrating different techniques to help you to solve all your math questions.  

Our website helps students gain understanding and self-confidence in math. The sessions help students in understanding mathematical concepts. We have panel of experts to guide you to achieve the best.  For immediate assistance you may log into your session and avail guidance. Start asking questions the moment you find yourself “stuck”.

Online Tutoring supports you with all possible math helpOnline tutoring websites are revolutionizing the notion of education. With the increasing number of students getting conscious about the importance of education, the technology has gained recognition. The technology helps the student to interact with an online expert and resolve those doubts that he is unable to deal with.

Tutor Pace is the world’s leading pioneer when it comes to study online.

Use Online Calculators To Make Your Math Questions Interactive And Fun!

Learn Algebra 2 online from Math experts. Our free Algebra 2 tutorials conducted by Math experts help you to understand how online tutoring session works. The sessions cover Algebra 2 formulas, lessons, equations and concepts. Our Algebra 2 online tutorials are planned after extensive research and they are designed to help you master in the subject. Practice different problems with experts and resolve your doubts. Work on simple and complicated problems and get first-hand answers on how to resolve them.

TutorPace is an online tutoring website that provides sessions to cover both basic and advanced topics. There are test sessions that help you to solve problems and help you review the concepts you learn.

Explore online tutoring and get homework help, help for test preparation. Register and get answer to all your math questions. Convey your doubts to an online math tutor to get all your questions answered. Online tutoring can be done from the comfort of home. A lot of online tutoring sites also proffer homework and assignment help making it much easier for you to get your assignments ready on time.

Some topics covered in our Algebra 2 tutorial:

  • Linear Equations
  • Functions
  • Graphing functions
  • Simultaneous Equations
  • Quadratic functions
  • Relations and functions

So, what are you waiting for? Book the best tutor now!