log-3-x-logx-solve-for-X-

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

\log^{3} \sqrt{} x = \sqrt{logx}

solve for X

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

\frac{1}{3} l o g x = {(l o g x)}^{\frac{1}{2}}

y = {(l o g x)}^{\frac{1}{2}}

\frac{1}{3} y^{2} = y \Rightarrow y^{2} - 3 y = 0 \Rightarrow y = 0, y = 3

i f y = 0 \Rightarrow {(l o g x)}^{\frac{1}{2}} = 0 \Rightarrow l o g x = 0 \Rightarrow x = 1

i f y = 3 \Rightarrow {(l o g x)}^{\frac{1}{2}} = 3 \Rightarrow l o g x = 9 \Rightarrow x = 10^{9}

Commented by solomonwells last updated on 28/May/22

thanks sir