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Question Number 158366 by HongKing last updated on 03/Nov/21

Answered by MathsFan last updated on 03/Nov/21

$$\frac{\mathrm{lne}}{\mathrm{lnx}\bullet \mathrm{lnx}}+\frac{\mathrm{lne}}{(\mathrm{lne}-\mathrm{lnx})(\mathrm{lne}-\mathrm{lnx})}=8$$$$\mathrm{say}\mathrm{a}=\mathrm{lnx}$$$$\frac{1}{{\mathrm{a}}^2}+\frac{1}{1-2\mathrm{a}+{\mathrm{a}}^2}=8$$$${2\mathrm{a}}^2-2\mathrm{a}-7=0$$$$\mathrm{a}=\frac{1\pm \sqrt{15}}{2}$$$$\mathrm{lnx}=\frac{1\pm \sqrt{15}}{2}$$$$\mathrm{x}={\mathrm{e}}^{\frac{1\pm \sqrt{15}}{2}}$$

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