Question

$\log_{128} 32$

Explanation:

Step1: Express bases as powers of 2

$128=2^7$, $32=2^5$

Step2: Rewrite log with new bases

$\log_{2^7} 2^5$

Step3: Apply log power rule

$\frac{5}{7}\log_{2} 2$

Step4: Simplify $\log_{2}2=1$

$\frac{5}{7} \times 1$

Answer:

$\frac{5}{7}$