CAT 2019 Question Paper | Quants Slot 2

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Question 1 : The real root of the equation 2^6x + 2^3x+2 - 21 = 0 is

1. $\frac{log_{2}3}{3}$
2. log₂9
3. $\frac{log_{2}7}{3}$
4. log₂27

Video Explanation

Explanatory Answer

Given equation - 2^6x + 2^3x+2 - 21 = 0
The idea is to convert the above equation to a quadratic one.
So, 2^6x =
Let y =
Now, 2^6x + 2^3x+2 - 21 = 0 can be rewritten as + 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 = => y should always be positive
Therefore, y = -7 is not a valid solution. So, only y = +3 exists.
= 3
Taking log on both sides,
=
3x =
x = , which is the real solution to the given equation

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

Hence, the answer is $\frac{log_{2}3}{3}$

Choice A is the correct answer.

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