What is the value of log4 16?

asked Feb 2, 2023 171k views

2 votes

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4 votes

Answer:

$\log_416=2$

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:

$\implies \log_416=2$

Oboe answered Feb 6, 2023

by Oboe

2.9k points

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