Solve for :
I know 9 is 3^2 and 4 is 2^2
but how can i simplify this while knowing the above?
If you use the rule I suggested then you get:
$\displaystyle 9^{9x-3}=4^{8x-2}$
$\displaystyle \Leftrightarrow \log(9^{9x-3})=\log(4^{8x-2})$
$\displaystyle \Leftrightarrow (9x-3)\log(9)=(8x-2)\log(4)$
$\displaystyle \Leftrightarrow 9x\log(9)-3\log(9)=8x\log(4)-2\log(4)$
$\displaystyle \Leftrightarrow 9x\log(9)-8x\log(4)=3\log(9)-2\log(4)$
$\displaystyle \Leftrightarrow x[9\log(9)-8\log(4)]=3\log(9)-2\log(4)$
$\displaystyle \Leftrightarrow ...$