Posted by **Sunny** on Wednesday, January 4, 2012 at 5:18am.

Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.

3^x-70*3^-x=9

- college algebra -
**Reiny**, Wednesday, January 4, 2012 at 8:20am
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.

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