Witam, proszę o szybkie rozwiązanie rownań logarytmicznych:     [latex]b) (lnx)(1+lnx)=2+lnx^2[/latex]   [latex]c) 2log3 - frac{1}{2}log_{0,1}x=log_{100}0,5[/latex]   [latex]d) log_{0,2}49 + 2log_{25}x = 3log_{125}7[/latex]   [latex]e) 1-lnx=3ln2[/latex]

[latex] lnx + (lnx)^2=2+2lnx\ lnx=y \y+y^2=2+2y\y^2-y-2=0\y_{1}=-1; y_{2}=2\x=e^{y}\x_{1}=e^{-1};x_{2}=e^2 \\ c) 2log3- frac{1}{2}frac{log_{10}{x}}{log_{10}{0,1}}=frac{log_{10}{0,5}}{log_{10}{100}}\ 2log3-frac{1}{2} frac{log_{10}{x}}{-1}=frac{-log2}{log2}\2log3+log(sqrt{x})=-1 \ 2log3+log(sqrt{x})=log10^{-1} \ log(9sqrt{x})=log(10^{-1}) \9sqrt{x}=10^{-1} \ sqrt{x} =frac{1}{90} \ x=90^{-2} [/latex] [latex] d) log_{0,2}{49}=log_{5^{-1}}{49}=frac{log_{7}{49}}{log_{7}{5^{-1}}}=frac{2}{-log_{7}{5}}=-2log_{5}{7}\ log_{125}{7}=frac{log_{5}{7}}{log_{5}{125}}=frac{log_{5}{7}}{3}\ log_{25}{x}=frac{log_{5}{x}}{log_{5}{25}}=frac{log_{5}{x}}{2} \ -2log_{5}{7}+2*frac{log_{5}{x}}{2}=3*frac{log_{5}{7}}{3}\log_{5}{x}=3log_{5}{7}\x=7^3 [/latex] [latex] e) 1=ln(e); ln(e)-ln(x)=ln(2^3)\frac{e}{x}=8 \ x=frac{e}{8} [/latex]