Question

which equation is equivalent to \\(\log_{x} 36 = 2\\)?\
\\(36^{x} = 2\\)\
\\(x^{2} = 36\\)\
\\(2^{x} = 36\\)\
\\(x^{2} = 36^{2}\\)

Explanation:

Step1: Recall logarithm definition

The logarithmic equation $\log_{a}b = c$ is equivalent to the exponential equation $a^{c}=b$ by the definition of logarithms.

Step2: Apply definition to given log

Given $\log_{x}36 = 2$, here $a = x$, $b = 36$, $c = 2$. Using the definition, we get $x^{2}=36$.

Answer:

$\boldsymbol{x^{2}=36}$ (the option with text "x² = 36")