Question
Download Solution PDFयदि f(x) = log x है तो f(xy) और f(x/y) का समांतर माध्य क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
समांतर माध्य एक आकड़ों के समूह में संख्याओं की मात्रा से विभाजित उस समूह में सभी संख्याओं का योग होता है।
दो धनात्मक संख्या a और b का समांतर माध्य \(\rm \frac{{a\; + \;b}}{2}\) है।
लघुगुणक सूत्र
log mn = log m + log n
\( \rm \log (\frac{m}{n}) = \log m - \ log n\)
गणना:
दिया गया है: f(x) = log x
निम्न को ज्ञात करने के लिए: f(xy) और f(x/y) का समांतर माध्य
f(xy) = log (xy) = log x + log y (∵ log mn = log m + log n)
\( \rm f(\frac{x}{y}) = \log (\frac{x}{y}) = \log x - \ log y\)
अब, f(xy) और f(x/y) का समांतर माध्य = \(\rm \frac{f(xy)+f(\frac{x}{y})}{2}\)
\(= \rm \frac{\log x+ \log y + \log x - \log y}{2}\\ = \frac{2\log x}{2} \\= \log x\)
Last updated on Jun 20, 2025
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