solve-log-x-10-log-x-2-10-6-

Question Number 171847 by Mikenice last updated on 21/Jun/22

s o l v e :

{l o g}_{x} 10 + {l o g}_{x^{2}} 10 = 6

Commented by kaivan.ahmadi last updated on 21/Jun/22

{l o g}_{x} 10 + \frac{1}{2} {l o g}_{x} 10 = 6 \Rightarrow \frac{3}{2} {l o g}_{x} 10 = 6 \Rightarrow

{l o g}_{x} 10 = 4 \Rightarrow x^{4} = 10 \Rightarrow x = \sqrt[4]{10}

Answered by cherokeesay last updated on 21/Jun/22

\Leftrightarrow \frac{l n 10}{l n x} + \frac{l n 10}{2 l n x} = 6 (x > 0)

\frac{3 l n 10}{2 l n x} = 6 \Leftrightarrow 10 = x^{4} \Leftrightarrow

x_{1} = \sqrt[4]{10}, x_{2} = \sqrt[4]{10} i