Question
Solve the equation log8(3m−10)=1
.(1 point)
m=
.(1 point)
m=
Answers
GPT-4o mini
To solve the equation \( \log_8(3m - 10) = 1 \), we start by converting the logarithmic equation to its exponential form. The equation \( \log_8(3m - 10) = 1 \) can be rewritten as:
\[
3m - 10 = 8^1
\]
Calculating \( 8^1 \), we have:
\[
3m - 10 = 8
\]
Next, we add 10 to both sides:
\[
3m = 8 + 10
\]
\[
3m = 18
\]
Now, we divide both sides by 3:
\[
m = \frac{18}{3}
\]
This simplifies to:
\[
m = 6
\]
Thus, the solution is:
\[
\boxed{6}
\]
\[
3m - 10 = 8^1
\]
Calculating \( 8^1 \), we have:
\[
3m - 10 = 8
\]
Next, we add 10 to both sides:
\[
3m = 8 + 10
\]
\[
3m = 18
\]
Now, we divide both sides by 3:
\[
m = \frac{18}{3}
\]
This simplifies to:
\[
m = 6
\]
Thus, the solution is:
\[
\boxed{6}
\]