two questons, are they both quadratic? if anyone could get me started much appreciated.

(a) $\displaystyle 3{^2{^x}}+ 8 . 3{^x}-9=0$ (multiply 8 x 3x)

(b) $\displaystyle e{^2{^x}}+ 8e{^x}=3^2 $

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- Feb 10th 2010, 04:51 AMdecoy808quadratic?
two questons, are they both quadratic? if anyone could get me started much appreciated.

(a) $\displaystyle 3{^2{^x}}+ 8 . 3{^x}-9=0$ (multiply 8 x 3x)

(b) $\displaystyle e{^2{^x}}+ 8e{^x}=3^2 $ - Feb 10th 2010, 04:58 AMRaoh
- Feb 10th 2010, 05:05 AMdanielomalmsteen
b)

define $\displaystyle e^x = u$ then the equation is equivalent to $\displaystyle u^2+8u-9=0$

Factoring

$\displaystyle (u+9)(u-1)=0$

solutions $\displaystyle u=1$ and $\displaystyle u=-9$

As the exponential negative values does not yield, the solution is

$\displaystyle u=1=e^x \rightarrow x=0$