Question 193270
{{{5^(x-1)=3^x}}} Start with the given equation.



{{{log(10,(5^(x-1)))=log(10,(3^x))}}} Take the log of both sides



{{{(x-1)log(10,(5))=x*log(10,(3))}}} Pull down the exponents



{{{x*log(10,(5))-log(10,(5))=x*log(10,(3))}}} Distribute



{{{-log(10,(5))=x*log(10,(3))-x*log(10,(5))}}} Subtract {{{x*log(10,(5))}}} from both sides.



{{{-log(10,(5))=x(log(10,(3))-log(10,(5)))}}} Factor out the GCF "x" on the right side



{{{-log(10,(5))=x*log(10,(3/5))}}} Combine the logs on the right side using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}



{{{-log(10,(5))/log(10,(3/5))=x}}} Divide both sides by {{{log(10,(3/5))}}}.



{{{3.15066=x}}} Evaluate the right side (using a calculator). Note: the value of "x" is now approximate



{{{x=3.15066}}} Rearrange the equation



So the solution is approximately {{{x=3.15066}}}