SOLUTION: If 9^(2x+1)=81^(x-2)/3^x find x

Algebra ->  Exponents -> SOLUTION: If 9^(2x+1)=81^(x-2)/3^x find x      Log On


   

Question 984472: If 9^(2x+1)=81^(x-2)/3^x find x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

9%5E%282x%2B1%29=81%5E%28x-2%29%2F3%5Ex
to find x, convert all in same base
%283%5E2%29%5E%282x%2B1%29=%283%5E4%29%5E%28x-2%29%2F3%5Ex
3%5E%282%282x%2B1%29%29=3%5E%284%28x-2%29%29%2F3%5Ex
3%5E%284x%2B2%29=3%5E%284x-8%29%2F3%5Ex
3%5E%284x%2B2%29=3%5E%284x-8-x%29
3%5E%284x%2B2%29=3%5E%283x-8%29........if bases same, then we have
4x%2B2=3x-8......solve for x
4x-3x=-8-2
x=-10