Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.
3^x-70*3^-x=9
multiply each term by 3^x
3^(2x) - 70 = 9(3^x)
(3^x)^2 - 9(3^x) - 70=0
let 3^x = y , our equation becomes
y^2 - 9y - 70 = 0
(y-14)(y+5) = 0
y = 14 or y = -5
then
3^x = 14
log (3^x) = log14
xlog3 = log14
x = log14/log3 or appr. 2.402
or e^x = -5, which has no solution.