यदि xyyx = 1 है, तो (1, 1) पर किसके बराबर है?

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NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)
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  1. -1
  2. 0
  3. 1
  4. 4

Answer (Detailed Solution Below)

Option 1 : -1
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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प्रयुक्त सूत्र:

  1. log mn = log m + log n 
  2. log mn = n log m
  3. 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,

 (y log x) +  (x log y) = 0 

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 , -1 के बराबर है।

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