Question

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

Explanation:

Step1: Recall Logarithm Definition

The logarithmic equation \(\log_b(a) = c\) is equivalent to the exponential equation \(b^c = a\) by the definition of logarithms.

Step2: Apply Definition to Given Equation

For the equation \(\log_3(x + 5)=2\), we identify \(b = 3\), \(a=x + 5\), and \(c = 2\). Using the logarithm - to - exponential conversion formula \(b^c=a\), we substitute the values: \(3^2=x + 5\).

Answer:

\(3^{2}=x + 5\) (the third option among the given choices)