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?
$\displaystyle \displaystyle 4^x - 3\cdot 2^x + 2 = 0$
$\displaystyle \displaystyle \left(2^2\right)^x - 3\cdot 2^x + 2 = 0$
$\displaystyle \displaystyle 2^{2x} - 3\cdot 2^x + 2 = 0$
$\displaystyle \displaystyle \left(2^x\right)^2 - 3\cdot 2^x + 2 = 0$.
Let $\displaystyle \displaystyle X = 2^x$ so that the equation becomes
$\displaystyle \displaystyle X^2 - 3X + 2 = 0$.
You should be able to solve for $\displaystyle \displaystyle X$ and use this to solve for $\displaystyle \displaystyle x$.