The real root of the equation | Quantitative Aptitude – Logarithm

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The question below is from previous year CAT question from CAT 2019 exam comes from Logarithm: The real root of the equation. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot -2 - Question 3 - The real root of the equation

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

1. log(base2)3 / 2

2. log(base2)9

3. log(base2)27

4. log(base2)7 / 3

Show Answer

Let 2^(3x) = k

So given equation 2^6x + 2^(3x+2) – 21 =0

Or (2^3x)^2 + 4*2^3x -21 =0

Or k^2 + 4k -21 =0

(k+7)*(k-3) =0

k = -4 or 3

k= -4 is not possible

so k =3

or 2^3x = 3

taking log of both sides 3x * log 2 = log 3

3x = log 3 / log 2

3x = log(base2)⁡3

Or x = (log(base2⁡)3) /3

Option a) (log(base2)⁡3) /3

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