Question 6

Solve for $x$ :
$\begin{array}{l} 8^{2 x - 10} = 9^{8 x - 2} \\ x = ◻ \end{array}$

You may enter the exact value or round to 4 decimal places.
Question Help:
Video
Submit Question
Jump to Answer

Answer

Expert–verified

Hide Steps

Answer

$x = \log {(\frac{32768}{9})}^{\frac{1}{\log (\frac{8}{6561})}}$

Steps

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

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

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

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