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?
log(base2)3 / 2
log(base2)9
log(base2)27
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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