Logarithmus-Gleichung

[Christian Kruse]

你好 MudGuard,

10^(lg5*lg(x-3) + lg2*lg(2x-1)) = 10^(5*lg2*lg5)

[latex]10^(\log_{10}5 * \log_{10}(x-3) + \log_{10}2 * \log_{10}(2x-1)) = 10^(5*log_{10}2 * \log_{10}5)[/latex]

10^(lg5*lg(x-3)) * 10^(lg2*lg(2x-1)) = 10^(5*lg2*lg5)

[latex]10^(\log_{10}5*\log_{10}(x-3)) * 10^(\log_{10}2*\log_{10}(2x-1)) = 10^(5*\log_{10}2*\log_{10}5)[/latex]

Umformung a^(b*c) = (a^b)^c

[latex]a^{b*c} = (a^b)^c[/latex]

10^(lg(x-3))^lg5 * 10^(lg(2x-1))^lg2 = 10^(5*lg2*lg5)

[latex]10^{(\log_{10}(x-3))^{\log_{10}5}} * 10^{{\log_{10}(2x-1)}^{\log_{10}2}} = 10^{5*\log_{10}2*\log_{10}5}[/latex]

Exponent und Logarithmus rauswerfen
(x-3)^lg5 * (2x-1)^lg2 = 10^(5*lg2*lg5)

latex^{\log_{10}5} * (2x-1)^{\log_{10}2} = 10^{5*\log_{10}2*\log_{10}5}[/latex]

Hoffentlich hab ich mich nirgends vertippt...

再见,
克里斯蒂安