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Question Number 170661 by solomonwells last updated on 28/May/22

log^3 (√)x   =   (√(logx))  solve  for      X

$$\boldsymbol{\mathrm{log}}\:^{\mathrm{3}} \sqrt{}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\sqrt{\boldsymbol{\mathrm{logx}}} \\ $$$$\boldsymbol{\mathrm{solve}}\:\:\boldsymbol{\mathrm{for}}\:\:\:\:\:\:\boldsymbol{{X}} \\ $$$$ \\ $$

Commented by kaivan.ahmadi last updated on 28/May/22

(1/3)logx=(logx)^(1/2)   y=(logx)^(1/2)   (1/3)y^2 =y⇒y^2 −3y=0⇒y=0 ,y=3  if y=0⇒(logx)^(1/2) =0⇒logx=0⇒x=1  if y=3⇒(logx)^(1/2) =3⇒logx=9⇒x=10^9

$$\frac{\mathrm{1}}{\mathrm{3}}{logx}=\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${y}=\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}{y}^{\mathrm{2}} ={y}\Rightarrow{y}^{\mathrm{2}} −\mathrm{3}{y}=\mathrm{0}\Rightarrow{y}=\mathrm{0}\:,{y}=\mathrm{3} \\ $$$${if}\:{y}=\mathrm{0}\Rightarrow\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{0}\Rightarrow{logx}=\mathrm{0}\Rightarrow{x}=\mathrm{1} \\ $$$${if}\:{y}=\mathrm{3}\Rightarrow\left({logx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{3}\Rightarrow{logx}=\mathrm{9}\Rightarrow{x}=\mathrm{10}^{\mathrm{9}} \\ $$

Commented by solomonwells last updated on 28/May/22

thanks  sir

$$\mathrm{thanks}\:\:\mathrm{sir}\:\: \\ $$

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