Question 64649
{{{3^(x-1) = 2}}} Take the loarithm of both sides.
{{{(x-1)log((3)) = log((2))}}} Divide both sides by log(3).
{{{x-1 = (log((2)))/log((3))}}} Add 1 to both sides.
{{{x = (log((2)))/log((3)) + 1}}} Evaluate using your calculator.
{{{x = 0.630929 + 1}}}
{{{x = 1.6309}}} to four decimal places.

Check:
{{{3^(x-1) = 2}}} Substitute x = 1.6309
{{{3^0.6309 = 1.9999346}}} This is very close to 2.