CA Foundation Exam > CA Foundation Questions > If logx logy=log(x y),y can be expressed as?
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If logx logy=log(x y),y can be expressed as?
Most Upvoted Answer
If logx logy=log(x y),y can be expressed as?
Logx+logy=log(x+y)
log(xy)=log (x+y) ; [logab =loga+ logb]
xy=x+y xy-y=x y(x-1)=x y= x/(x-1)
log(xy)=log (x+y) ; [logab =loga+ logb]
xy=x+y xy-y=x y(x-1)=x y= x/(x-1)
Community Answer
If logx logy=log(x y),y can be expressed as?
Solution:
Given logx logy = log(x y)
We need to find y in terms of x.
We can use the logarithmic identity loga b = loga c + loga d, where b = c * d.
Applying this identity, we get:
logx logy = log(x y)
logx logy = logx + logy
logy - logx = logx
logy = logx + logx
logy = 2 logx
Therefore, y = 10^(2 logx)
Simplifying further using the logarithmic identity loga b^c = c loga b, we get:
y = 10^(2 logx)
y = 10^(logx + logx)
y = 10^logx * 10^logx
y = x * x
y = x^2
Hence, y can be expressed as x^2.
Conclusion:
Therefore, we have found that y can be expressed as x^2.
Given logx logy = log(x y)
We need to find y in terms of x.
We can use the logarithmic identity loga b = loga c + loga d, where b = c * d.
Applying this identity, we get:
logx logy = log(x y)
logx logy = logx + logy
logy - logx = logx
logy = logx + logx
logy = 2 logx
Therefore, y = 10^(2 logx)
Simplifying further using the logarithmic identity loga b^c = c loga b, we get:
y = 10^(2 logx)
y = 10^(logx + logx)
y = 10^logx * 10^logx
y = x * x
y = x^2
Hence, y can be expressed as x^2.
Conclusion:
Therefore, we have found that y can be expressed as x^2.
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If logx logy=log(x y),y can be expressed as?
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If logx logy=log(x y),y can be expressed as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If logx logy=log(x y),y can be expressed as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If logx logy=log(x y),y can be expressed as?.
If logx logy=log(x y),y can be expressed as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If logx logy=log(x y),y can be expressed as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If logx logy=log(x y),y can be expressed as?.
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