Question 9 of 10 , Step 1 of 1
$7 / 10$
Correct
Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places.
\[
7^{2 x-6}=536
\]
Answer
Final Answer: The exact expression for $x$ is $4.614703064301705$ and the decimal approximation rounded to two decimal places is $\boxed{4.61}$
Step 1 ：Rewrite the equation as $2x - 6 = \frac{\ln(536)}{\ln(7)}$
Step 2 ：Calculate the natural logarithm of both sides: $\ln(536) = 6.284134161070802$ and $\ln(7) = 1.9459101490553132$
Step 3 ：Solve for x: $x = \frac{\ln(536) / \ln(7) + 6}{2} = 4.614703064301705$
Step 4 ：Final Answer: The exact expression for $x$ is $4.614703064301705$ and the decimal approximation rounded to two decimal places is $\boxed{4.61}$
