Question:
The real root of the equation $2^{6 x}+2^{3 x+2}-21=0$ is
- $\frac{\log _{2} 7}{3}$
- $\log _{2} 9$
- $\frac{\log _{2} 3}{3}$
- $\log _{2} 27$
Correct Answer: Option: 3
$2^{6 x}+2^{3 x} \times 2^{2}-21=0$
Take $2^{3 x}=y$
$\Rightarrow y^{2}+4 y-21=0$
$\Rightarrow(y-3)(y+7)=0$
$\Rightarrow y=3$ or $y=-7$
$\Rightarrow 2^{3 x}=3$ or $2^{3 x}=-7\{\text { No solution }\}$
$\Rightarrow 3 x=\log _{2}{3}$
$\Rightarrow x=\frac{log _{2}{3}}{3}$
CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions
