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 can rewrite it in exponential form. The equation states that the logarithm base 8 of \( (3m - 10) \) equals 1, which means:
\[
3m - 10 = 8^1
\]
Calculating \( 8^1 \):
\[
3m - 10 = 8
\]
Now, add 10 to both sides to isolate the term with \( m \):
\[
3m = 8 + 10
\]
\[
3m = 18
\]
Next, divide both sides by 3 to solve for \( m \):
\[
m = \frac{18}{3}
\]
\[
m = 6
\]
Thus, the solution is:
\[
\boxed{6}
\]
\[
3m - 10 = 8^1
\]
Calculating \( 8^1 \):
\[
3m - 10 = 8
\]
Now, add 10 to both sides to isolate the term with \( m \):
\[
3m = 8 + 10
\]
\[
3m = 18
\]
Next, divide both sides by 3 to solve for \( m \):
\[
m = \frac{18}{3}
\]
\[
m = 6
\]
Thus, the solution is:
\[
\boxed{6}
\]