# 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 # 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

## 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.

Examples:

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

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

• 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

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

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. 10 miles is the answer

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

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Read more – Top 10 Tips To Help With Math Homework

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