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Question Number 206177 by MATHEMATICSAM last updated on 08/Apr/24

$$\mathrm{Find}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{solutions}\mathrm{of}$$$$\mathrm{the}\mathrm{equation}\sin x=\log x.$$

Answered by Frix last updated on 08/Apr/24

$$\log x=\ln x?$$$$-1⩽\ln x⩽1\iff {\mathrm{e}}^{-1}⩽x⩽\mathrm{e}$$$$\Rightarrow \mathrm{one}\mathrm{solution}\mathrm{at}x\approx 2.21910715$$$$$$$$\log x={\log }_{10}x?$$$$-1⩽\log x⩽1\iff \frac{1}{10}⩽c⩽10$$$$\Rightarrow \mathrm{three}\mathrm{solutions}$$$$x_1\approx 2.69625656$$$$x_2\approx 7.32834778$$$$x_3\approx 8.26382974$$

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