# Logarithmic Form

How to change an equation in exponent form to logarithmic form (and vice versa): definition, 6 examples, and their solutions.

## Definition

A logarithm (log) is a way

to write the exponent.

For example,

if 2^{[exponent]} = 3,

then the exponent is log_{2} 3.

log_{2} 3 is read as

[log base 2 of 3].

## Example2^{4} = 16 → Logarithmic Form

2^{4} = 16

The exponent is 4.

So 4 = log_{2} 16.

So

4 = log_{2} 16

is the answer.

## Example3^{-2} = 1/9 → Logarithmic Form

3^{-2} = 1/9

The exponent is -2.

So -2 = log_{3} 1/9.

Negative Exponent

So

-2 = log_{3} 1/9

is the answer.

## Example5^{1/2} = √5 → Logarithmic Form

5^{1/2} = √5

The exponent is 1/2.

So 1/2 = log_{5} √5.

Rational Exponent

So

1/2 = log_{5} √5

is the answer.

## Example2 = log_{3} 9 → Exponential Form

2 = log_{3} 9

The exponent is 2.

The base is 3.

So 3^{2} = 9.

So

3^{2} = 9

is the answer.

## Example-5 = log_{2} 1/32 → Exponential Form

-5 = log_{2} 1/32

The exponent is -5.

The base is 2.

So 2^{-5} = 1/32.

So

2^{-5} = 1/32

is the answer.

## Example2/3 = log_{7} ^{3}√49 → Exponential Form

2/3 = log_{7} ^{3}√49

The exponent is 2/3.

The base is 7.

So 7^{2/3} = ^{3}√49.

So

7^{2/3} = ^{3}√49

is the answer.