Question Number 181579 by mathlove last updated on 27/Nov/22
$$\left(\sqrt[{\mathrm{3}}]{{x}}\right)^{−\mathrm{2}+{log}_{{x}} \mathrm{11}} =\mathrm{11} \\ $$$${x}=? \\ $$
Commented by Socracious last updated on 27/Nov/22
$$\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{11}} \\ $$
Answered by Frix last updated on 27/Nov/22
$${x}>\mathrm{0} \\ $$$${x}^{−\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{ln}\:\mathrm{11}}{\mathrm{3ln}\:{x}}} =\mathrm{11} \\ $$$${x}^{−\frac{\mathrm{2}}{\mathrm{3}}} {x}^{\frac{\mathrm{ln}\:\mathrm{11}}{\mathrm{3ln}\:{x}}} =\mathrm{11} \\ $$$${x}^{−\frac{\mathrm{2}}{\mathrm{3}}} \mathrm{11}^{\frac{\mathrm{1}}{\mathrm{3}}} =\mathrm{11} \\ $$$${x}^{−\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{11}^{\frac{\mathrm{2}}{\mathrm{3}}} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{11}} \\ $$
Commented by mathlove last updated on 27/Nov/22
$${way}\:\:{x}^{\frac{{ln}\mathrm{11}}{\mathrm{3}{lnx}}} \overset{?} {=}\mathrm{11}^{\frac{\mathrm{1}}{\mathrm{3}}} ? \\ $$
Commented by mathlove last updated on 27/Nov/22
$${thanks} \\ $$