Question 17039
Try this.

{{{2^x = 3^(x-1)}}} Take the log of both sides.
{{{xlog2 = (x-1)log3}}}Expand the right side.
{{{xlog2 = xlog3 - log3}}} Subtract xlog3 from both sides.
{{{xlog2 - xlog3 = -log3}}} Factor an x on the left side.
{{{x(log2 - log3) = -log3}}} Divide both sides by (log2 - log3)
{{{x = (-log3)/(log2 - log3)}}} You could just work it out on your calculator.
{{{x = 2.71}}}