Formation of a Differential Equation from a General Solution
The value of ...
Question
The value of xlny−lnz⋅ylnz−lnx⋅zlnx−lny is
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Solution
let t=xlny−lnz⋅ylnz−lnx⋅zlnx−lny Taking logarithm on both sides, we get lnt=(lny−lnz)lnx+(lnz−lnx)lny+(lnx−lny)lnz ⇒lnt=lnylnx−lnzlnx+lnzlny−lnxlny+lnxlnz−lnylnz=0 ⇒t=1 Ans: 1