SSC CGL Exam > SSC CGL Questions > The simplified form of log(75/16) -2 log(5/9)...
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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?
Verified Answer
The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?a)log 2...
= log75/16 - 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2
Most Upvoted Answer
The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?a)log 2...
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.
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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