Question

Solve the equation log8 (3m−10)=1
.

Answer 1

To solve the equation \( \log_8(3m - 10) = 1 \), we will first rewrite the logarithmic equation in its exponential form. The equation states that \( 3m - 10 \) is equal to \( 8 \) raised to the power of \( 1 \).

Rewriting the equation:

\[
3m - 10 = 8^1
\]

This simplifies to:

\[
3m - 10 = 8
\]

Next, we will isolate \( m \) in this equation. First, we add \( 10 \) to both sides:

\[
3m = 8 + 10
\]

This simplifies to:

\[
3m = 18
\]

Now, we divide both sides by \( 3 \):

\[
m = \frac{18}{3}
\]

Simplifying this gives:

\[
m = 6
\]

Finally, we can verify our solution by plugging \( m = 6 \) back into the original logarithmic equation:

Calculating \( 3m - 10 \):

\[
3(6) - 10 = 18 - 10 = 8
\]

Now checking the logarithm:

\[
\log_8(8) = 1
\]

Since this is true, our solution is confirmed. Thus, the final answer is:

\[
\boxed{6}
\]