Question 17.

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

A

\log_{2}{9}

B

\frac{\log_{2}{3}}{3}

C

\log_{2}{27}

D

\frac{\log_{2}{7}}{3}

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Text Explanation

Let $2^{3x}$ = v

$2^{6x} + 2^{3x + 2} - 21 = 0$

= $v^2+4v-21=0$

=(v+7)(v-3)=0

v=3, -7

$2^{3x}$ = 3 or $2^{3x}$ = -7(This can be negated)

3x= $\log_23$

x= $\log_23$ /3

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