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CAT 2019 Quant Question with Solution 47

Question:
The real root of the equation $2^{6 x}+2^{3 x+2}-21=0$ is

  1. $\frac{\log _{2} 7}{3}$
  2. $\log _{2} 9$
  3. $\frac{\log _{2} 3}{3}$
  4. $\log _{2} 27$
Show Answer

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 $2^{3 x}=-7\{\text { No solution }\}$

$\Rightarrow 3 x=\log _{2}{3}$

$\Rightarrow x=\frac{log _{2}{3}}{3}$


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