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Question Number 103766 by bramlex last updated on 17/Jul/20

given  { ((x = ln 34)),((y = ln 38)) :}  find ln 32 in terms of x and y

$${given}\:\begin{cases}{{x}\:=\:\mathrm{ln}\:\mathrm{34}}\\{{y}\:=\:\mathrm{ln}\:\mathrm{38}}\end{cases} \\ $$$${find}\:\mathrm{ln}\:\mathrm{32}\:{in}\:{terms}\:{of}\:{x}\:{and}\:{y}\: \\ $$

Answered by Dwaipayan Shikari last updated on 17/Jul/20

e^x =34  e^y =38  e^y −e^x =4  8(e^y −e^x )=32  log(8(e^y −e^x ))=log32

$${e}^{{x}} =\mathrm{34} \\ $$$${e}^{{y}} =\mathrm{38} \\ $$$${e}^{{y}} −{e}^{{x}} =\mathrm{4} \\ $$$$\mathrm{8}\left({e}^{{y}} −{e}^{{x}} \right)=\mathrm{32} \\ $$$${log}\left(\mathrm{8}\left({e}^{{y}} −{e}^{{x}} \right)\right)={log}\mathrm{32} \\ $$

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