Question
Solve x
log8(3x+13)=2
log8(3x+13)=2
Answers
GPT-4o mini
To solve the equation \( \log_8(3x + 13) = 2 \), we can rewrite the logarithmic equation in exponential form. The equation states that \( 3x + 13 \) is equal to \( 8^2 \).
1. Rewrite in exponential form:
\[
3x + 13 = 8^2
\]
2. Calculate \( 8^2 \):
\[
8^2 = 64
\]
3. Substitute this back into the equation:
\[
3x + 13 = 64
\]
4. Isolate \( 3x \) by subtracting 13 from both sides:
\[
3x = 64 - 13
\]
\[
3x = 51
\]
5. Divide both sides by 3 to solve for \( x \):
\[
x = \frac{51}{3}
\]
\[
x = 17
\]
Thus, the solution is:
\[
\boxed{17}
\]
1. Rewrite in exponential form:
\[
3x + 13 = 8^2
\]
2. Calculate \( 8^2 \):
\[
8^2 = 64
\]
3. Substitute this back into the equation:
\[
3x + 13 = 64
\]
4. Isolate \( 3x \) by subtracting 13 from both sides:
\[
3x = 64 - 13
\]
\[
3x = 51
\]
5. Divide both sides by 3 to solve for \( x \):
\[
x = \frac{51}{3}
\]
\[
x = 17
\]
Thus, the solution is:
\[
\boxed{17}
\]