Question

which equation is equivalent to \\(\log_{3}(x + 5) = 2\\)?
\\(\circ\\) \\(3^{2} = \left\log_{3}(x + 5)\
ight^{3}\\)
\\(\circ\\) \\(2^{3} = \left\log_{3}(x + 5)\
ight^{2}\\)
\\(\circ\\) \\(3^{2} = x + 5\\)
\\(\circ\\) \\(2^{3} = x + 5\\)

Explanation:

Step1: Recall Logarithm Definition

The definition of a logarithm states that if $\log_b(a) = c$, then $b^c = a$.

Step2: Apply Definition to Given Equation

For the equation $\log_3(x + 5) = 2$, where $b = 3$, $a = x + 5$, and $c = 2$. Using the logarithm definition, we rewrite it as $3^2 = x + 5$.

Answer:

$3^2 = x + 5$ (the third option)