Quantitative Aptitude – logarithm – The value of log(base a)(a/b)+log(base b)(b/a)


Slot – 2 – Quantitative Aptitude – logarithm – The value of log(base a)(a/b)+log(base b)(b/a)


Q. The value of log(base a)(a/b)+log(base b)(b/a), for 1 < a ≤ b cannot be equal to?
  1. 0
  2. -0.5
  3. 1
  4. -1
Answer: 1

Solutions:
log(base a)(a/b) +log(base b)(⁡b/a)
= 1 – log_a⁡b+1- log_b⁡a
= 2 – (log(base a)⁡b+ log(base b)⁡a)
= 2 – (log(base a⁡)b+1/(log(base a⁡)b) )
Now as x +1/x≥2 for all the positive values of x .
So 2 – (log(base a)⁡ b+1/(log(base a)⁡ b) ) will always be less than or equal to zero. Thus it can never be equal to 1.
Option 3) is correct.

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