Question

the smallest value of x that satisfies the equation 2^2x - 8 * 2^x = -12 is ?

please answer fast

Answer 1

$\textbf{Given:}$

$2^{2x}-8(2^x)+12=0$

$\textbf{To find:}$

$\text{The smallest value of x satisfying the given equation}$

$\textbf{Solution:}$

$2^{2x}-8(2^x)+12=0$

$(2^x)^2-8(2^x)+12=0$

$t^2-8t+12=0$ $\text{where t=2^x }$

$(t-6)(t-2)=0$

$\implies\,t=2,6$

$\text{when t=2,}$

$\implies\,2^x=2$

$\implies\boxed{\bf\,x=1}$

$\text{when t=6,}$

$\implies\,2^x=6$

$\implies\,2^x=2^{log_26}$

$\implies\,x=log_26$

$\implies\,x=log_2(2{\times}3)$

$\implies\,x=log_22+log_23$

$\implies\,x=1+log_23$

$\implies\boxed{\bf\,x=1+log_23}$

$\text{Comparing the values of x,}$

$\textbf{The least value of x satisfying the given equation is 1}$

$\textbf{Find more:}$

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