CA Foundation Exam > CA Foundation Questions > If log (2a - 3b) = log a - log b, then a =a)3...
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If log (2a - 3b) = log a - log b, then a =
- a)3b2 / 2b-1
- b)3b / 2b-1
- c)b2 / 2b+1
- d)3b2 / 2b+1
Correct answer is option 'A'. Can you explain this answer?
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If log (2a - 3b) = log a - log b, then a =a)3b2 / 2b-1b)3b/ 2b-1c)b2 /...
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If log (2a - 3b) = log a - log b, then a =a)3b2 / 2b-1b)3b/ 2b-1c)b2 /...
Solution:
Given, log (2a - 3b) = log a - log b
Using, log (a/b) = log a - log b
We get, log [(2a - 3b)/b] = log a
Taking antilog on both sides, we get
(2a - 3b)/b = a
Simplifying the above equation, we get
2a/b - 3 = a/b
2a/b - a/b = 3
a/b = 3
a = 3b
Substituting the value of a in option (A), we get
a = 3b
∴ 3b2/2(3b) - 1 = 3b2/6b - 1 = 3b2/5b = 3b/5
Therefore, option (A) is correct.
Given, log (2a - 3b) = log a - log b
Using, log (a/b) = log a - log b
We get, log [(2a - 3b)/b] = log a
Taking antilog on both sides, we get
(2a - 3b)/b = a
Simplifying the above equation, we get
2a/b - 3 = a/b
2a/b - a/b = 3
a/b = 3
a = 3b
Substituting the value of a in option (A), we get
a = 3b
∴ 3b2/2(3b) - 1 = 3b2/6b - 1 = 3b2/5b = 3b/5
Therefore, option (A) is correct.
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Community Answer
If log (2a - 3b) = log a - log b, then a =a)3b2 / 2b-1b)3b/ 2b-1c)b2 /...
2a-3b=a/b
2a=a/b+3b
2a=a+3b2/b
2ab=a+3b2
2ab-a=3b2
a(2b-1)=3b2
a=3b2/2b-1
answer=a)
2a=a/b+3b
2a=a+3b2/b
2ab=a+3b2
2ab-a=3b2
a(2b-1)=3b2
a=3b2/2b-1
answer=a)
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If log (2a - 3b) = log a - log b, then a =a)3b2 / 2b-1b)3b/ 2b-1c)b2 / 2b+1d)3b2 / 2b+1Correct answer is option 'A'. Can you explain this answer?
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