# Logarithmic Form

How to write equations in exponential form to logarithmic form and vice versa: definition, examples, and their solutions.

## Definition

Logarithm is a way

to write the [exponent] of a number.

For 2^{0} = 1,

the exponent is 0.

So 0 = log_{2} 1.

For 2^{1} = 2,

the exponent is 1.

So 1 = log_{2} 2.

By the same way,

for 2^{[blue]} = 3,

the exponent is [blue].

So [blue] = log_{2} 3.

[log_{2} 3] is read as [log base 2 of 3].

## Example 1: Logarithmic Form of 2^{4} = 16

2^{4} = 16

The exponent is 4.

So 4 = log_{2} 16.

## Example 2: Logarithmic Form of 3^{-2} = 1/9

3^{-2} = 1/9

The exponent is -2.

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

Negative exponent

## Example 3: Logarithmic Form of 5^{1/2} = √5

5^{1/2} = √5

The exponent is 1/2.

So 1/2 = log_{5} √5.

Rational exponents

## Example 4: Exponential Form of 2 = log_{3} 9

2 = log_{3} 9

The exponent is 2.

So 3^{2} = 9.

## Example 5: Exponential Form of -5 = log_{2} (1/32)

-5 = log_{2} (1/32)

The exponent is -5.

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

## Example 6: Exponential Form of 2/3 = log_{7} ^{3}√49

2/3 = log_{7} ^{3}√49

The exponent is 2/3.

So 7^{2/3} = ^{3}√49.