CAT 2019 Shift 2 Paper

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Question : 82 of 100

Marks: +1, -0

The real root of the equation

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

is

$\log_2 27$
${\log_2 3}/3$
${\log_2 7}/3$
${\log_2 9}$

Solution:

2^{6 x}+2^{3 x} × 2^{2}-21=0

Take

2^{3 x}=y

⇒ y^{2}+4 y-21=0

⇒(y-3)(y+7)=0

⇒ y=3

or

y=-7

⇒ 2^{3 x}=3

or

2^{3 x}=-7\{

No solution

\}

⇒ 3 x=\log _{2} 3

⇒ x=\;{\log _{2} 3}/{3}

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