Solve
points
Part 1 of 2
Points: 0 of 1
Save
Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give an exact answer.
\[
\log _{9} x+\log _{9}(8 x-1)=1
\]
Rewrite the given equation without logarithms. Do not solve for $\mathrm{x}$.
Answer
Rewrite the equation in exponential form to remove the logarithm using the property: \(\log_b(a) = c\) is equivalent to \(b^c = a\). This gives us the final equation without logarithms: \(\boxed{9^1 = x(8x - 1)}\).
Step 1 ：Combine the two logarithms on the left side of the equation into a single logarithm using the property of logarithms: \(\log_b(a) + \log_b(c) = \log_b(ac)\). This gives us \(\log_9(x(8x - 1)) = 1\).
Step 2 ：Rewrite the equation in exponential form to remove the logarithm using the property: \(\log_b(a) = c\) is equivalent to \(b^c = a\). This gives us the final equation without logarithms: \(\boxed{9^1 = x(8x - 1)}\).
