Question 972068
{{{2^(x-1) = 3^(2x+1)}}}



{{{log((2^(x-1))) = log((3^(2x+1)))}}}	Apply logs to both sides (to isolate exponents)



{{{(x-1)*log((2)) = (2x+1)*log((3))}}}	Use rule 3 (from <a href="http://www.purplemath.com/modules/logrules.htm">this link</a>)



{{{x*log((2))-log((2)) = 2x*log((3))+log((3))}}}	Distribute



{{{x*log((2)) = 2x*log((3))+log((3))+log((2))}}}	Add {{{log((2))}}} to both sides.



{{{x*log((2))-2x*log((3)) = log((3))+log((2))}}}	Subtract {{{2x*log((3))}}} from both sides.



{{{x(log((2))-2*log((3))) = log((3))+log((2))}}}	Factor out the GCF x



{{{x = (log((3))+log((2)))/(log((2))-2*log((3)))}}}	Divide both sides by {{{log((2))-2*log((3))}}} to isolate x.



{{{x = (log((2))+log((3)))/(log((2))-2*log((3)))}}}	Rearrange terms. This is the exact answer in terms of logs.



{{{x = -1.19126813092756}}}	Use a calculator to get the approximate answer



{{{x = -1.191}}}	Round to 3 decimal places (again this is approximate)