Question

Solve the following equation:
$2^{2x+1}-{33.2}^{x-1}+4=0$

Answer 1

$2^{2x+1}-33\cdot 2^{x-1}+4=0$

$2\cdot 2^{2x}-\frac{33}{2}\cdot 2^x+4=0$(quadratic equation in $2^x$)

$2^x=\frac{33}{4}\pm \sqrt{\frac{\frac{(1089-128)}{4}}{16}}$

$2^x=\frac{33}{4}\pm \frac{31}{2\left(4\right)}$

$2^x=\frac{1}{8}\left(35\right),\frac{1}{8}\left(97\right)$

$\Rightarrow$ By taking ${\log }_{10}$ on both the sides,

$x\log 2=\log \frac{35}{8}$

$x\log 2=\log \frac{97}{8}$

$x=\frac{\log \frac{97}{8}}{\log 2}$ and $x=\frac{\log \frac{35}{8}}{\log 2}$