# Logarithm of a Product

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

## Formula

log_{a} xy = log_{a} x + log_{a} y

You can split the log of a product like this.

## Examplelog_{2} 3 = a, log_{2} 24 = ?

Solution

Solution (Detail)

Write the prime factorization of 24.

24 = 2^{3}⋅3

log_{2} 2^{3}⋅3 = log_{2} 2^{3} + log_{2} 3

log_{2} 2^{3} = 3 log_{2} 2

Logarithm of a Power

log_{2} 3 = a

So

log_{2} 2^{3} + log_{2} 3

= 3 log_{2} 2 + a.

log_{2} 2 = 1

Logarithm of Itself

3⋅1 + a = a + 3

So a + 3 is the answer.