sorry about the double
Hey I was wondering if you could help me find the answer to some practice questions we were given. I have a quiz tomorrow morning but I'm not even sure if I'm doing it right. Whats the point of practice questions if I don't even have the answers
I'm asked to solve exponential equations here are two of the more difficult ones I'm not sure how to do:
Could really use a small explanation, or just the steps alone so I can interpret it myself
$2^{x+3}-2^x=224$
$2^x\cdot 2^3 - 2^x = 224$
$2^x\left(2^3-1\right)=224$
Spoiler:
$4\left(2^{2x}\right)+31\left(2^x\right)-8=0$
$4\left(2^x\right)^2 + 31\left(2^x\right)-8=0$
let $u=2^x$
$4u^2+31u-8=0$
$(8+u)(4u-1)=0$
$u=\{-8, \frac{1}{4}\}$
as $u=2^x>0, u=-8\mbox{ can be disregarded.}$
$2^x=\frac{1}{4}$
$x=-2$