Question

The value of $x$ satisfying the equation $2^{2x}-8\times 2^x=-12$ 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)

The correct options are
A $1+\frac{\log 3}{\log 2}$
D $1$

$2^{2x}-8.2^x=-12let{2}^x=t,t>0t^2-8t+12=0(t-2)(t-6)=0\therefore t=2or62^x=2or{2}^x=6x=1orx\log 2=\log 6orx=\frac{\log 3+\log 2}{\log 2}x=1+\frac{\log 3}{\log 2}$