Question

If $4^x-4^{x-1}=24$, then $x$ is $\frac{m}{2}$. The value of $m$ is

Answer 1

$4^x-4^x\times 4^{-1}=24$

$\Rightarrow 4^x(1-\frac{1}{4})=24$

$\Rightarrow 4^x\left(\frac{4-1}{4}\right)=24$

$=4^x=\frac{24\times 4}{3}$

$\Rightarrow 4^x=32$

$=2^{2x}=2^5$

$\Rightarrow x=\frac{5}{2}$