Question

The value of x satisfying the equation
$2^{2x}-8\cdot 2^x=-12$, is

• A. $1+\frac{\log 3}{\log 2}$
• B. $\frac{1}{2}\log 6$
• C. $1+\log \frac{3}{2}$
• D. 1

Answer 1

Answer: (A), (D)

$2^x=t$
$t^2-8t+12=0$
$(t-6)(t-2)=0$
$2^x=6\Rightarrow x={\log }_{2}6=1+\frac{\log 3}{\log 2}\Rightarrow (A)$
$2^x=2\Rightarrow x=1\Rightarrow (D)$