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?
0
-0.5
1
-1
Answer: 1
Solutions:
log(base a)(a/b) +log(base b)(b/a)
= 1 – log_ab+1- log_ba
= 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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