what is the value of $log_{6}\frac{1}{36}$?\n-6\n-2\n2\n6

Explanation:

Step1: Rewrite the fraction

We know that $\frac{1}{36}=6^{-2}$ since $6^2 = 36$. So, $\log_{6}\frac{1}{36}=\log_{6}6^{-2}$.

Step2: Use the logarithm property

The property of logarithms $\log_{a}a^{x}=x$. Here $a = 6$ and $x=-2$. So, $\log_{6}6^{-2}=-2$.

Answer:

-2