Question 122246
{{{9^(3x-1)=81^(-x+1)}}}
{{{9^(3x-1)=(9^2)^(-x+1)}}} Substitute for 81.
{{{9^(3x-1)=(9^(2*(-x+1)))}}} Rule for multiplying exponents.
{{{(3x-1)=2*(-x+1)}}} Take log base 9 of each side.
{{{3x-1=-2x+2}}}
{{{5x=3}}}
{{{x=3/5}}}
Check your answer.
{{{9^(3x-1)=81^(-x+1)}}}
{{{9^(3(3/5)-1)=81^((-3/5)+1)}}}
{{{9^(9/5-5/5)=81^(2/5)}}}
{{{9^(4/5)=81^(2/5)}}}
{{{5.80=5.80}}}