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rahul85

Oct. 3, 2020, 11:05 p.m.

The real root of the equation 2^6x + 2^(3x+2) - 21 = 0 is

This question was asked in CAT-2019

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

quant

cat-2019

logarithm

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ANSWERS

Keval123

Oct. 4, 2020, 12:51 a.m.

Given equation - 2^6x + 2^3x+2 - 21 = 0

The idea is to convert the above equation to a quadratic one.

So, 2^6x= (2^3x)²
Let y = 2^3x

Now, 2^6x + 2^3x+2 - 21 = 0 can be rewritten as (2^3x)²+ 2².2^3x - 21 = 0
y² + 4y - 21 = 0

Solving the above quadratic equation,
(y + 7) (y - 3) = 0
So, y = -7 or +3
y = 2^3x=> y should always be positive

Therefore, y = -7 is not a valid solution. So, only y = +3 exists.
2^3x= 3

Taking log on both sides,
log₂2^3x = log₂3
3x = log₂3
x = (log₂3)/3

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