Question Number 170661 by solomonwells last updated on 28/May/22
$$\boldsymbol{\mathrm{log}}\:^{\mathrm{3}} \sqrt{}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\sqrt{\boldsymbol{\mathrm{logx}}} \\ $$$$\boldsymbol{\mathrm{solve}}\:\:\boldsymbol{\mathrm{for}}\:\:\:\:\:\:\boldsymbol{{X}} \\ $$$$ \\ $$
Commented by kaivan.ahmadi last updated on 28/May/22
$$\frac{\mathrm{1}}{\mathrm{3}}{logx}=\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${y}=\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}{y}^{\mathrm{2}} ={y}\Rightarrow{y}^{\mathrm{2}} −\mathrm{3}{y}=\mathrm{0}\Rightarrow{y}=\mathrm{0}\:,{y}=\mathrm{3} \\ $$$${if}\:{y}=\mathrm{0}\Rightarrow\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{0}\Rightarrow{logx}=\mathrm{0}\Rightarrow{x}=\mathrm{1} \\ $$$${if}\:{y}=\mathrm{3}\Rightarrow\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{3}\Rightarrow{logx}=\mathrm{9}\Rightarrow{x}=\mathrm{10}^{\mathrm{9}} \\ $$
Commented by solomonwells last updated on 28/May/22
$$\mathrm{thanks}\:\:\mathrm{sir}\:\: \\ $$