Question
Download Solution PDFयदि xyyx = 1 है, तो (1, 1) पर
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
- log mn = log m + log n
- log mn = n log m
- खण्डशः अवकलन:
गणना:
दिया गया है कि
xyyx = 1
दोनों पक्षों पर log लेने पर,
log( xyyx) = log 1
चूँकि, log mn = log m + log n है।
⇒ log xy + log yx = log 1
चूँकि log mn = n log m
⇒ y log x + x log y = 0 (∵ log 1 = 0)
x के सापेक्ष अवकलन करने पर,
⇒
खण्डशः अवकलन का उपयोग करने पर,
⇒
सूत्र (4) और (5) का प्रयोग करने पर,
⇒
⇒
⇒
उपरोक्त अवकलन में x = y = 1 रखने पर,
⇒
अतः (1, 1) पर
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