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Question Number 181579 by mathlove last updated on 27/Nov/22

$${\left(\sqrt[3]{x}\right)}^{-2+{log}_{x}11}=11$$$$x=?$$

Commented by Socracious last updated on 27/Nov/22

$$\mathbf{x}=\frac{1}{11}$$

Answered by Frix last updated on 27/Nov/22

$$x>0$$$$x^{-\frac{2}{3}+\frac{\ln 11}{3\ln x}}=11$$$$x^{-\frac{2}{3}}{x}^{\frac{\ln 11}{3\ln x}}=11$$$$x^{-\frac{2}{3}}{11}^{\frac{1}{3}}=11$$$$x^{-\frac{2}{3}}={11}^{\frac{2}{3}}$$$$x=\frac{1}{11}$$

Commented by mathlove last updated on 27/Nov/22

$$way{x}^{\frac{ln11}{3lnx}}\stackrel{?}{=}{11}^{\frac{1}{3}}?$$

Commented by mathlove last updated on 27/Nov/22

$$thanks$$

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