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Question Number 81437 by jagoll last updated on 13/Feb/20

$$5{}^{\mathrm{lnx}}=50-{\mathrm{x}}^{\ln 5}$$$$$$

Commented by john santu last updated on 13/Feb/20

$$\mathrm{formula}{\mathrm{a}}^{{\log }_{\mathrm{b}}\mathrm{c}}={\mathrm{c}}^{{\log }_{\mathrm{b}}\mathrm{a}}$$$$\Rightarrow 5^{\ln \mathrm{x}}=50-5^{\ln \mathrm{x}}$$$$2.5^{\ln \mathrm{x}}=50\Rightarrow 5^{\ln \mathrm{x}}=5^{\ln \mathrm{x}}=5^2$$$$\ln \mathrm{x}=2\Rightarrow {\mathrm{e}}^{\ln \mathrm{x}}={\mathrm{e}}^2$$$$\therefore \mathrm{x}={\mathrm{e}}^2.$$

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