Question

What is the value of log4 16?

Answer 1

`\log_416=2`

Explanation:

Given expression:

`\log_416`

Rewrite 16 as 4²:

`\implies \log_44^2`

`\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax`

`\implies 2 \log_44`

`\textsf{Apply log law}: \quad \log_aa=1`

`\implies 2 \cdot 1`

Simplify

`\implies 2`

Therefore:

`\implies \log_416=2`