Logarithmic Form

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

Definition

Definition

A logarithm (log) is a way
to write the exponent.

For example,
if 2[exponent] = 3,
then the exponent is log2 3.

log2 3 is read as
[log base 2 of 3].

Example 1

Example

Solution

24 = 16

The exponent is 4.

So 4 = log2 16.

So
4 = log2 16
is the answer.

Example 2

Example

Solution

3-2 = 1/9

The exponent is -2.

So -2 = log3 1/9.

Negative Exponent

So
-2 = log3 1/9
is the answer.

Example 3

Example

Solution

51/2 = √5

The exponent is 1/2.

So 1/2 = log55.

Rational Exponent

So
1/2 = log55
is the answer.

Example 4

Example

Solution

2 = log3 9

The exponent is 2.
The base is 3.

So 32 = 9.

So
32 = 9
is the answer.

Example 5

Example

Solution

-5 = log2 1/32

The exponent is -5.
The base is 2.

So 2-5 = 1/32.

So
2-5 = 1/32
is the answer.

Example 6

Example

Solution

2/3 = log7 349

The exponent is 2/3.
The base is 7.

So 72/3 = 349.

So
72/3 = 349
is the answer.