Logarithm of a Product

How to solve the logarithm of a product (loga xy): formula, 1 example, and its solution.

Formula

Formula

loga xy = loga x + loga y

You can split the log of a product like this.

Example

Example

Solution

Write the prime factorization of 24.

24 = 23⋅3

log2 23⋅3 = log2 23 + log2 3

log2 23 = 3 log2 2

Logarithm of a Power

log2 3 = a

So
log2 23 + log2 3
= 3 log2 2 + a.

3⋅1 + a = a + 3

So a + 3 is the answer.