# Math Help - Solve 4^x - 3.2^x + 2 = 0.

1. ## Solve 4^x - 3.2^x + 2 = 0.

here it is:
4^x - 3.2^x + 2 = 0

i have a complete mindblank when i try and solve this....
can anyone help me out?

2. $\displaystyle 4^x - 3\cdot 2^x + 2 = 0$

$\displaystyle \left(2^2\right)^x - 3\cdot 2^x + 2 = 0$

$\displaystyle 2^{2x} - 3\cdot 2^x + 2 = 0$

$\displaystyle \left(2^x\right)^2 - 3\cdot 2^x + 2 = 0$.

Let $\displaystyle X = 2^x$ so that the equation becomes

$\displaystyle X^2 - 3X + 2 = 0$.

You should be able to solve for $\displaystyle X$ and use this to solve for $\displaystyle x$.