Question 840033
{{{10^(3x-8)=2^(5-x)}}}
take log of each side
{{{log((10^(3x-8)))=log((2^(5-x)))}}}
{{{(3x-8)*log((10))=(5-x)*log((2)))}}}
{{{(3x-8)*(log(2)+log(5)))=(5-x)*log((2)))}}}
{{{(3x-8)*log(2) + (3x-8)*log(5)=(5-x)*log(2)}}}
{{{(3x-8)*log(5)=(5-x)*log(2)-(3x-8)*log(2)}}}
{{{(3x-8)*log(5)=(13-4x)*log(2)}}}
{{{3*log(5)*x-8*log(5)=13*log(2)-4*log(2)*x}}}
{{{3*log(5)*x+4*log(2)*x=13*log(2)+8*log(5)}}}
{{{(3*log(5)+4*log(2))*x=13*log(2)+8*log(5)}}}
{{{x=(13*log(2)+8*log(5))/(3*log(5)+4*log(2))}}}
check out http://www.wolframalpha.com/input/?i=10^%283x-8%29%3D2^%285-x%29