Question

$\log_{27}9$

Explanation:

Step1: Express bases as powers of 3

$27 = 3^3$, $9 = 3^2$
So $\log_{27}9 = \log_{3^3}3^2$

Step2: Apply logarithm power rule

Use $\log_{a^m}a^n = \frac{n}{m}$
$\log_{3^3}3^2 = \frac{2}{3}$

Answer:

$\frac{2}{3}$