college algebra
posted by Sunny
Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.
3^x70*3^x=9

Reiny
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
(y14)(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.
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