Help!

1. 2^(2x) + 4 =17 x (times) 2^ (x-1)

i have been taught to find a common expression and denote it as y

i.e. 3 ^2x -10 times 3 ^x + 9=0; y= 3^x

but do not know how to do that here

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- Apr 14th 2010, 01:27 AMsarahhardtkeExponential Equation
Help!

1. 2^(2x) + 4 =17 x (times) 2^ (x-1)

i have been taught to find a common expression and denote it as y

i.e. 3 ^2x -10 times 3 ^x + 9=0; y= 3^x

but do not know how to do that here - Apr 14th 2010, 01:34 AMe^(i*pi)

Note that $\displaystyle 2^{x-1} = 2^x \cdot 2^{-1} = \frac{1}{2}\,2^x$

$\displaystyle 2^{2x} + 4 = \frac{17}{2} \cdot 2^x$

$\displaystyle 2^{2x} - \frac{17}{2}\,2^x + 4 =0$

This is now in the form of a quadratic equation in $\displaystyle 2^x$ so you can use the quadratic formula.

Recall that for all real x: $\displaystyle 2^x > 0$