Question

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

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation $\log_b(y) = x$ is equivalent to the exponential equation $b^x = y$.

Step2: Apply the definition to the given equation

For the equation $\log_3(x + 5) = 2$, we have $b = 3$, $x = 2$, and $y = x + 5$. Using the definition $b^x = y$, we substitute the values: $3^2 = x + 5$.

Answer:

$3^2 = x + 5$ (the fourth option in the list of choices)