Logarithmic Form

Logarithmic Form

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

Definition

Logarithm is a way to write the exponent of a number.

Logarithm is a way to write
the exponent of a number.

The exponent 0 satisfies 20 = 1.
So 0 = log2 1.

The exponent 1 satisfies 21 = 2.
So 1 = log2 2.

The exponent 2 satisfies 22 = 4.
So 2 = log2 4.

Likewise,
the exponent 'log2 3' is a number
that satisfies 2log2 3 = 3.
(log2 3 = 1.585..., 21.585... = 3)

And the exponent 'log2 5' is a number
that satisfies 2log2 5 = 5.
(log2 5 = 2.322..., 22.322... = 5)

log2 3 is read "log base 2 of 3".

Example 1

Write each equation in logarithmic form. 1. 2^4 = 16, 2. 3^-2 = 1/9, 3. 5^(1/2) = sqrt(5)

The exponent 4 satisfies 24 = 16.

So 4 = log2 16.

The exponent -2 satisfies 3-2 = 1/9.

So -2 = log3 (1/9).

The exponent 1/2 satisfies 51/2 = √5.

So 1/2 = log55.

Example 2

Write each equation in exponential form. 1. 2 = log_3 9, 2. -5 = log_2 (1/32), 3. 2/3 = log_7 (cube root(49))

The exponent is 2.

So 32 = 9.

The exponent is -5.

So 2-5 = 1/32.

The exponent is 2/3.

So 72/3 = 349.