Question Number 103766 by bramlex last updated on 17/Jul/20
$${given}\:\begin{cases}{{x}\:=\:\mathrm{ln}\:\mathrm{34}}\\{{y}\:=\:\mathrm{ln}\:\mathrm{38}}\end{cases} \\ $$$${find}\:\mathrm{ln}\:\mathrm{32}\:{in}\:{terms}\:{of}\:{x}\:{and}\:{y}\: \\ $$
Answered by Dwaipayan Shikari last updated on 17/Jul/20
$${e}^{{x}} =\mathrm{34} \\ $$$${e}^{{y}} =\mathrm{38} \\ $$$${e}^{{y}} −{e}^{{x}} =\mathrm{4} \\ $$$$\mathrm{8}\left({e}^{{y}} −{e}^{{x}} \right)=\mathrm{32} \\ $$$${log}\left(\mathrm{8}\left({e}^{{y}} −{e}^{{x}} \right)\right)={log}\mathrm{32} \\ $$