# Exponential Equation

• April 14th 2010, 02:27 AM
sarahhardtke
Exponential 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
• April 14th 2010, 02:34 AM
e^(i*pi)
Quote:

Originally Posted by sarahhardtke
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

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

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

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

This is now in the form of a quadratic equation in $2^x$ so you can use the quadratic formula.
Recall that for all real x: $2^x > 0$