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Question-208139




Question Number 208139 by efronzo1 last updated on 06/Jun/24
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Answered by Ghisom last updated on 06/Jun/24
x>0  ((ln (x^2 +1) +ln x)/(ln 5 +ln 2))=((ln x)/(ln 2))  ((ln (x^2 +1))/(ln x))=((ln 5)/(ln 2))  obviously x=2
$${x}>\mathrm{0} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{5}\:+\mathrm{ln}\:\mathrm{2}}=\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:\mathrm{5}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\mathrm{obviously}\:{x}=\mathrm{2} \\ $$

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