i'm confused on:
x=log (base 4)51.6
and 5^2x=9^x-1
thanks in advance.
i think i'm just overthinking.
$\displaystyle 5^{2x} = 9^{x - 1}$
take the log of both sides
$\displaystyle \Rightarrow \ln 5^{2x} = \ln 9^{x - 1}$
$\displaystyle \Rightarrow 2x \ln 5 = (x - 1) \ln 9$
$\displaystyle \Rightarrow 2x \ln 5 = x \ln 9 - \ln 9$
$\displaystyle \Rightarrow 2x \ln 5 - x \ln 9 = - \ln 9$
$\displaystyle \Rightarrow x (2 \ln 5 - \ln 9) = - \ln 9$
$\displaystyle \Rightarrow x = \frac {- \ln 9}{2 \ln 5 - \ln 9}$
and you can simplify that a bit if you want
don't let the logs confuse you. the log of a constant is a constant (provided the constant is greater then zero, of course). how would you do this if all the logs you saw were constants. you'd get the terms with x's on one side of the equation, and everything else on the other side. then you'd factor out the x and divide both sides by its coefficient