Matematică, întrebare adresată de Piciucaty123, 9 ani în urmă

Log din baza x din 2 + Log din baza radical x din 2=9

Răspunsuri la întrebare

Răspuns de ruginadenisacp9no6r
2
Aceasta este rezolvarea.
Anexe:

Piciucaty123: Log din baza x din radx de unde vine?
Piciucaty123: Mi-am dat seaman
madaapissip9ny93: Felicitari.Varianta cea mai simpla si corecta
Răspuns de EnglishzzBoi
0
\log _x\left(2\right)+\log _{\sqrt{x}}\left(2\right)=9 \\  \\ \log _{\sqrt{x}}\left(2\right)=\frac{\ln \left(2\right)}{\ln \left(\sqrt{x}\right)} \\  \\ \log _x\left(2\right)+\frac{\ln \left(2\right)}{\ln \left(\sqrt{x}\right)}=9 \\  \\ \log _x\left(2\right)=\frac{\ln \left(2\right)}{\ln \left(x\right)} \\  \\ \frac{\ln \left(2\right)}{\ln \left(x\right)}+\frac{\ln \left(2\right)}{\ln \left(\sqrt{x}\right)}=9 \\  \\ \ln \left(\sqrt{x}\right)=\frac{1}{2}\ln \left(x\right) \\  \\ \frac{\ln \left(2\right)}{\ln \left(x\right)}+\frac{\ln \left(2\right)}{\frac{1}{2}\ln \left(x\right)}=9 \\  \\ \ln \left(x\right)=u \\  \\ \frac{\ln \left(2\right)}{u}+\frac{\ln \left(2\right)}{\frac{1}{2}u}=9 \\  \\ \frac{\ln \left(2\right)}{u}\cdot \frac{u^2}{2}+\frac{\ln \left(2\right)}{\frac{1}{2}u}\cdot \frac{u^2}{2}=9\cdot \frac{u^2}{2} \\  \\ \frac{\ln \left(2\right)u}{2}+\ln \left(2\right)u=\frac{9u^2}{2} \\  \\ \frac{\ln \left(2\right)u}{2}+\ln \left(2\right)u=\frac{9u^2}{2} \\  \\ \frac{\ln \left(2\right)u}{2}\cdot \:2+\ln \left(2\right)u\cdot \:2=\frac{9u^2}{2}\cdot \:2 \\  \\ \ln \left(2\right)u+2\ln \left(2\right)u=9u^2 \\  \\ 3\ln \left(2\right)u=9u^2 \\  \\ 9u^2=3\ln \left(2\right)u \\  \\ 9u^2-3\ln \left(2\right)u=0 \\  \\ u=\frac{-\left(-3\ln \left(2\right)\right)+\sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0}}{2\cdot \:9} \\  \\ =\frac{3\ln \left(2\right)+\sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0}}{2\cdot \:9} \\  \\ =\frac{3\ln \left(2\right)+\sqrt{\left(-3\ln \left(2\right)\right)^2-0\cdot \:4\cdot \:9}}{18} \\  \\ \ln \left(2\right)+\sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0} \\  \\ =\frac{6\ln \left(2\right)}{18} \\  \\ =\frac{\ln \left(2\right)}{3} \\  \\ =\frac{3\ln \left(2\right)-\sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0}}{2\cdot \:9} \\  \\ =\frac{3\ln \left(2\right)-\sqrt{\left(-3\ln \left(2\right)\right)^2-0\cdot \:4\cdot \:9}}{18} \\  \\ 3\ln \left(2\right)-\sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0} \\  \\ \sqrt{\left(-3\ln \left(2\right)\right)^2-4\cdot \:9\cdot \:0}=\sqrt{\left(3\ln \left(2\right)\right)^2-0} \\  \\ =\sqrt{\left(3\ln \left(2\right)\right)^2} \\  \\ =3\ln \left(2\right) \\  \\ =3\ln \left(2\right)-3\ln \left(2\right)=0=\frac{0}{18}=0 \\  \\ u=\frac{\ln \left(2\right)}{3},\:u=0 \\  \\ u=\frac{\ln \left(2\right)}{3} \\  \\ \ln \left(x\right)=\frac{\ln \left(2\right)}{3} \\ \ln \left(x\right)=\frac{\ln \left(2\right)}{3} \\ \ln \left(x\right)=\ln \left(e^{\frac{\ln \left(2\right)}{3}}\right) \\ x=e^{\frac{\ln \left(2\right)}{3}}

ruginadenisacp9no6r: Mi se pare ca v ati complicat inutil cu niste calcule ,avand in vedere ca exista niste formule deduse deja. Cu drag , un student de la Facultatea de Matematica.
Alte întrebări interesante