Question
Download Solution PDFIf xyyx = 1, then what is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used :
- log mn = log m + log n
- log mn = n log m
- Differentiation by part:
Calculation :
Given that
xyyx = 1
Taking the log on both sides
log( xyyx) = log 1
Since, log mn = log m + log n
⇒ log xy + log yx = log 1
Since log mn = n log m
⇒ y log x + x log y = 0 (∵ log 1 = 0)
Diff. with resepct to x
⇒
Using differentiation by part
⇒
By using the formula (4) & (5)
⇒
⇒
⇒
Put x = y = 1 in above differential
⇒
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