Solve the exponential equation.
\[
3^{7 x-2}=7^{x}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is $\mathrm{x} \approx \square$.
(Type an integer or decimal rounded to three decimal places as needed.)
B. The solution is not a real number.
Answer
Final Answer: The solution is \(x \approx \boxed{0.383}\)
Step 1 ：Given the exponential equation \(3^{7x-2}=7^{x}\)
Step 2 ：Take the natural logarithm (ln) of both sides to bring down the exponents and solve for x
Step 3 ：Set up the equation as \(ln(3^{7x - 2}) = ln(7^{x})\)
Step 4 ：Solve the equation to get \(x = \frac{ln(3^{2})}{ln(\frac{2187}{7})}\)
Step 5 ：Evaluate the expression to get the numerical value of x
Step 6 ：Final Answer: The solution is \(x \approx \boxed{0.383}\)
