Question

$\log_{128} 16$

Explanation:

Step1: Express as same base

Rewrite 128 and 16 as powers of 2:
$128=2^7$, $16=2^4$, so $\log_{128}16=\log_{2^7}2^4$

Step2: Apply log power rule

Use $\log_{a^m}a^n=\frac{n}{m}$:
$\log_{2^7}2^4=\frac{4}{7}$

Answer:

$\frac{4}{7}$