To determine which equation is equivalent to [tex]\(\log_3(x + 5) = 2\)[/tex], let's rewrite this logarithmic equation in its exponential form.
The logarithmic equation [tex]\(\log_b(a) = c\)[/tex] can be rewritten as [tex]\(a = b^c\)[/tex].
So, starting with:
[tex]\[
\log_3(x + 5) = 2
\][/tex]
We can rewrite this as:
[tex]\[
x + 5 = 3^2
\][/tex]
Now, we need to compute [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Thus, the equation simplifies to:
[tex]\[
x + 5 = 9
\][/tex]
Among the provided choices, the equation [tex]\(x + 5 = 9\)[/tex] is equivalent to the third option:
[tex]\[
3^2 = x + 5
\][/tex]
So, the correct choice is:
3. [tex]\(3^2 = x + 5\)[/tex]
