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Question Number 171360 by Shrinava last updated on 13/Jun/22

$$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$${\log }_9\mathrm{x}\cdot {\log }_2(7-\mathrm{x})=1$$

Answered by MJS_new last updated on 13/Jun/22

$$\frac{\ln x}{2\ln 3}\times \frac{\ln (7-x)}{\ln 2}=1$$$$\ln x\ln (7-x)=2\ln 3\ln 2$$$$\ln x\ln (7-x)=\ln 3\ln 4$$$$\mathrm{obviously}\Rightarrow$$$$x_1=3$$$$x_2=4$$

Commented by Rasheed.Sindhi last updated on 14/Jun/22

$$\cap \mathbf{i}\subset \in \mathbf{sir}!$$

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