Question

b) 2^2x - 6.2^x +1 + 32 = 0 find creative section​

Answer 1

$\textbf{Given:}$

$2^{2x}-6.2^{x+1}+32=0$

$\textbf{To find:}$

$\text{The value of x}$

$\textbf{Solution:}$

$\text{Consider,}$

$2^{2x}-6.2^{x+1}+32=0$

$(2^x)^2-6.2^{x}2^1+32=0$

$(2^x)^2-12(2^x)+32=0$

$t^2-12t+32=-0\;\;\text{where}\;t=2^x$

$t^2-4t-8t+32=0$

$t(t-4)-8(t-4)=0$

$(t-8)(t-4)=0$

$\implies\,t=4,8$

$\begin{array}{|c|c|}\cline{1-2}\textbf{Case(i)}&\textbf{Case(ii)}\\\cline{1-2}&\\t=4&t=8\\2^x=4&2^x=8\\2^x=2^2&2^x=2^3\\\implies\bf\,x=2&\implies\bf\,x=3\\\cline{1-2}\end{array}$

$\textbf{Answer:}$

$\textbf{The values of x are 2 and 3}$.