Question

which statement is true for $\log_{3}(x + 1) = 2$?
\bigcirc $x + 1 = 3^{2}$
\bigcirc $x + 1 = 2^{3}$
\bigcirc $2(x + 1) = 3$
\bigcirc $3(x + 1) = 2$

Explanation:

Step1: Recall logarithm definition

The definition of a logarithm is: if $\log_{b}a = c$, then $a = b^{c}$.

Step2: Apply definition to given equation

Given $\log_{3}(x + 1)=2$, using the logarithm definition with $b = 3$, $a = x + 1$, and $c = 2$, we get $x + 1=3^{2}$.

Answer:

A. $x + 1 = 3^{2}$