Quantitative Aptitude – logarithm – If log(base a)30 = A


Slot – 3 – Quantitative Aptitude – logarithm – If log(base a)30 = A


Q. If log(base a)30 = A log(base a)(5/3)= -B and log(base 2)a=1/3, then log(base 3)a equals?
  1. A+B-3/2
  2. 2/A+B-3
  3. A+B/2 – 3
  4. 2/A+B – 3
Answer: 2

Solution:
Given, log(base a)⁡30=A , log(base a)5/3= -B and log(base 2)⁡a=1/3 or log(base a⁡)2=3
Now as we know 30 = 2*3*5 = 2*3^2 *5/3
Taking of both sides
log(base a⁡)30 = log(base a⁡) (2×3^2×5/3 )
A = log(base a)⁡2 + 2log(base a⁡)3+ log(base a⁡)5/3
A = 3 + 2 log(base a)3-B
log(base a)⁡3=(A+B-3)/2
So log(base 3) a=2/(A+B-3)


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