To solve the equation [tex]\(\log_5(x + 30) = 3\)[/tex], we need to convert the logarithmic equation into an exponential form.
1. Start with the given equation:
[tex]\[
\log_5(x + 30) = 3
\][/tex]
2. Recall that if [tex]\(\log_b(a) = c\)[/tex], then [tex]\(b^c = a\)[/tex]. In this case, [tex]\(b = 5\)[/tex], [tex]\(a = x + 30\)[/tex], and [tex]\(c = 3\)[/tex]. Therefore, we rewrite the equation as:
[tex]\[
5^3 = x + 30
\][/tex]
3. Calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
4. Now, the equation becomes:
[tex]\[
125 = x + 30
\][/tex]
5. To solve for [tex]\(x\)[/tex], subtract 30 from both sides:
[tex]\[
125 - 30 = x
\][/tex]
6. Perform the subtraction:
[tex]\[
125 - 30 = 95
\][/tex]
So, the solution is:
[tex]\[
x = 95
\][/tex]
Thus, the correct answer is [tex]\(x = 95\)[/tex].
