Question

evaluate $\log_{12}y^2$, given $\log_{12}y = 16$.

\\(\circ\\) 4

\\(\circ\\) 32

\\(\circ\\) 256

\\(\circ\\) 65,536

Explanation:

Step1: Recall logarithm power rule

The power rule of logarithms states that $\log_b a^n = n\log_b a$.

Step2: Apply the power rule to $\log_{12} y^2$

Using the power rule, we can rewrite $\log_{12} y^2$ as $2\log_{12} y$.

Step3: Substitute the given value

We know that $\log_{12} y = 16$, so substitute this into the expression: $2\times16 = 32$.

Answer:

32