Question

Sa se rezolve ecuația lg^2 x^2 +3lg 1/x=1??

Answer 1

$\lg x^2 \cdot \lg x^2+3\lg x^{-1}=1$

Conditii de existenta:
x > 0

$2\lg x\cdot 2\lg x-3\lg x = 1 \\ 4\lg^2x-3\lg x = 1 \\ Not\ \lg x = y \\ 4y^2-3y-1=0 \\ \Delta=9+16=25 \\ y_1= \frac{3-5}{8} =- \frac{1}{4}\Rightarrow x=10^{- \frac{1}{4}}= \frac{1}{ \sqrt[4]{10} } \\ y_2= \frac{3+5}{8} =1\Rightarrow x=10$