evaluate $\\log_{12}y^2$, given $\\log_{12}y = 16$.\n\n\\(\\circ\\) 4\n\n\\(\\circ\\) 32\n\n\\(\\circ\\)…
evaluate $\\log_{12}y^2$, given $\\log_{12}y = 16$.\n\n\\(\\circ\\) 4\n\n\\(\\circ\\) 32\n\n\\(\\circ\\) 256\n\n\\(\\circ\\) 65,536
Answer
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: $2\times16 = 32$.