Question 6 Solve for $x$ : \[ \begin{array}{l} 8^{2 x-10}=9^{8 x-2} \\ x=\square \end{array} \] You may enter the exact value or round to 4 decimal places. Question Help: Video Submit Question Jump to Answer

Step 1 ：Given the equation \(8^{2x - 10} = 9^{8x - 2}\)

Step 2 ：Take the natural logarithm on both sides to get \((2x - 10) \cdot \ln(8) = (8x - 2) \cdot \ln(9)\)

Step 3 ：Solve for x to get \(x = \log\left(\frac{32768}{9}\right)^{\frac{1}{\log\left(\frac{8}{6561}\right)}}\)

Step 4 ：\(\boxed{x = \log\left(\frac{32768}{9}\right)^{\frac{1}{\log\left(\frac{8}{6561}\right)}}}\)