Quantitative Aptitude – Algebra – Logarithm


Slot – 2 – Quantitative Aptitude – Algebra – Logarithm – The real root of the equation

Q. 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
Answer: log(base2)3 / 2

Solution: 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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