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Question Number 100150 by student work last updated on 25/Jun/20

$${\mathrm{x}}^{\ln }-{\mathrm{e}}^6\cdot \mathrm{x}=0\mathrm{x}=?$$$$\mathrm{help}\mathrm{me}$$

Commented by student work last updated on 25/Jun/20

$${\mathrm{x}}^{\mathrm{lnx}}-{\mathrm{e}}^6\cdot \mathrm{x}=0$$

Commented by bobhans last updated on 25/Jun/20

$$\mathrm{your}\mathrm{question}\mathrm{not}\mathrm{clear}$$

Commented by bemath last updated on 25/Jun/20

$$\ln \left({\mathrm{x}}^{\ln \mathrm{x}}\right)=\ln ({\mathrm{e}}^6.\mathrm{x})$$$${\left(\ln \left(\mathrm{x}\right)\right)}^2=6+\ln \left(\mathrm{x}\right)$$$${\mathrm{p}}^2-\mathrm{p}-6=0,\mathrm{p}=\ln \left(\mathrm{x}\right)$$$$(\mathrm{p}-3)(\mathrm{p}+2)=0$$$$\mathrm{p}=3\Rightarrow \ln \left(\mathrm{x}\right)=3,\mathrm{x}={\mathrm{e}}^3$$$$\mathrm{p}=-2\Rightarrow \ln \left(\mathrm{x}\right)=-2,\mathrm{x}={\mathrm{e}}^{-2}$$

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