Solve $7^{3 x-4}=3^{x-5}$ for $x$. Give both the exact answer and the decimal approximation to the nearest hundredth. If logarithms are needed to solve the equation, use "In." Exact answer: Decimal approximation: Question Help: $\square$ Video $D$ Post to forum Submit Question

Step 1 ：\(\ln(7^{3x-4}) = \ln(3^{x-5})\)

Step 2 ：\((3x-4)\ln(7) = (x-5)\ln(3)\)

Step 3 ：\(3x\ln(7) - 4\ln(7) = x\ln(3) - 5\ln(3)\)

Step 4 ：\(3x\ln(7) - x\ln(3) = 5\ln(3) + 4\ln(7)\)

Step 5 ：\(x(3\ln(7) - \ln(3)) = 5\ln(3) + 4\ln(7)\)

Step 6 ：\(x = \frac{5\ln(3) + 4\ln(7)}{3\ln(7) - \ln(3)}\)

Step 7 ：\(x \approx 3.47\)

Step 8 ：\(\boxed{x \approx 3.47}\)