All questions of Logarithms for RRB NTPC/ASM/CA/TA Exam

The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?
a)
log 2
b)
2 log 2
c)
log 3
d)
log 5
Correct answer is option 'A'. Can you explain this answer?

Ishaan Roy answered

Steps to simplify log(75/16) - 2 log(5/9) + log(32/343):
1. Use logarithmic properties:
- log(a/b) = log(a) - log(b)
- log(a^b) = b*log(a)
2. Apply the properties:
- log(75/16) - 2 log(5/9) + log(32/343)
= log(75) - log(16) - 2(log(5) - log(9)) + log(32) - log(343)
3. Further simplify:
= log(75) - log(16) - 2log(5) + 2log(9) + log(32) - log(343)
= log(75) - log(16) - log(5^2) + log(9^2) + log(32) - log(343)
= log(75) - log(16) - log(25) + log(81) + log(32) - log(343)
= log(75*81*32) - log(16*25*343)
= log(194400) - log(137600)
= log(194400/137600)
= log(1.4142)
= log(2)
Therefore, the simplified form of log(75/16) - 2 log(5/9) + log(32/343) is log 2.

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