Question

what is the value of $log_{6}\frac{1}{36}$?

$\boldsymbol{circ}$ $-6$
$\boldsymbol{circ}$ $-2$
$\boldsymbol{circ}$ $2$
$\boldsymbol{circ}$ $6$

Explanation:

Step1: Rewrite the argument

Rewrite \(\frac{1}{36}\) as a power of 6. We know that \(36 = 6^2\), so \(\frac{1}{36}=\frac{1}{6^2}=6^{-2}\).

Step2: Apply logarithm property

Using the property \(\log_a a^x = x\), for the logarithm \(\log_6 6^{-2}\), we have \(a = 6\) and \(x=-2\). So \(\log_6 6^{-2}=-2\).

Answer:

\(-2\) (corresponding to the option: \(-2\))