Question

solve for x.
\log_{x} \frac{1}{36} = 2
simplify your answer as much as possible.
x = \square

Explanation:

Step1: Convert log to exponential form

Recall the definition of a logarithm: if $\log_{a}b = c$, then $a^{c}=b$. For the equation $\log_{x}\frac{1}{36}=2$, we can rewrite it in exponential form as $x^{2}=\frac{1}{36}$.

Step2: Solve for x

To solve for $x$, we take the square root of both sides. Remember that when taking the square root, we consider both positive and negative roots, but since the base of a logarithm must be positive and not equal to 1, we discard the negative root. So, $x = \pm\sqrt{\frac{1}{36}}=\pm\frac{1}{6}$. But since $x>0$ and $x
eq1$, we have $x=\frac{1}{6}$.

Answer:

$\frac{1}{6}$