Logaritmi

Stefy Dum Feb 17, 2013 11:27 pm

1. $(2-log_{x}6)log_{x}6=\frac{3}{4}$

2. $x^{lgx}= 1000x^{2}$

Ma poate ajuta cineva? Sad

**Admin** Mier Feb 20, 2013 9:25 pm

Soluția completa problema 2:

$x^{\lg x}= 1000x^{2}\mid\textrm{\textbf{{\color{Red} logaritmam}}}:\\ \\ \lg x^{\lg x}=\lg 1000x^{2}\ \overset{\textrm{{\color{DarkRed} Proprietatea inmultirii logaritmi}}}{=}\ \lg 1000+\lg x^{2}\\ \\ =3+2\lg x\\ \\ \textrm{{\color{Emerald} \textbf{Sau}}}:\lg x\times \lg x=3+2\lg x\\ \\ \textrm{{\color{Emerald} \textbf{Sau}}}:\lg^{2}x=3+2\lg x\\ \\ \textrm{Notam cu}:\boxed{{\color{Magenta} \lg x=y}} \Rightarrow \textrm{ecuatia noastra devine:}\\ \\ y^{2}=3+2y\Rightarrow y_{1,2}=\left \{ -1,3 \right \}\Rightarrow \boxed{x=\left \{ {\color{Purple} 10^{-1},10^{3}} \right \}}$

**Admin** Mier Feb 20, 2013 9:26 pm

Problema 1 (mai simpla) tema!

Continut sponsorizat

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