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- https://query.libretexts.org/%E7%AE%80%E4%BD%93%E4%B8%AD%E6%96%87/%E4%B8%AD%E7%BA%A7%E4%BB%A3%E6%95%B0_(OpenStax)/10%3A_%E6%8C%87%E6%95%B0%E5%92%8C%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0/10.05%3A_10.5%EF%BC%9A%E4%BD%BF%E7%94%A8%E5%AF%B9%E6%95%B0%E7%9A%84%E5%B1%9E%E6%80%A7\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ...\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}\)
- https://query.libretexts.org/%D8%A7%D9%84%D9%84%D8%BA%D8%A9_%D8%A7%D9%84%D8%B9%D8%B1%D8%A8%D9%8A%D8%A9/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1_%D8%A7%D9%84%D9%85%D8%AA%D9%88%D8%B3%D8%B7_(OpenStax)/10%3A_%D8%A7%D9%84%D8%AF%D9%88%D8%A7%D9%84_%D8%A7%D9%84%D8%A3%D8%B3%D9%8A%D8%A9_%D9%88%D8%A7%D9%84%D9%84%D9%88%D8%BA%D8%A7%D8%B1%D9%8A%D8%AA%D9%85%D9%8A%D8%A9/10.05%3A_%D8%A7%D8%B3%D8%AA%D8%AE%D8%AF%D9%85_%D8%AE%D8%B5%D8%A7%D8%A6%D8%B5_%D8%A7%D9%84%D9%84%D9%88%D8%BA%D8%A7%D8%B1%D9%8A%D8%AA%D9%85%D8%A7%D8%AA\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ...\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}\)
- https://query.libretexts.org/Kiswahili/Algebra_ya_kati_(OpenStax)/10%3A_Kazi_za_kielelezo_na_za_Logarithmic/10.05%3A_Tumia_Mali_ya_Logarithms\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ...\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}\)
- https://query.libretexts.org/Idioma_Portugues/Algebra_intermediaria_(OpenStax)/10%3A_Fun%C3%A7%C3%B5es_exponenciais_e_logar%C3%ADtmicas/10.05%3A_Use_as_propriedades_dos_logaritmos\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ...\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}\)
- https://query.libretexts.org/Francais/Alg%C3%A8bre_interm%C3%A9diaire_(OpenStax)/10%3A_Fonctions_exponentielles_et_logarithmiques/10.05%3A_Utiliser_les_propri%C3%A9t%C3%A9s_des_logarithmes\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ...\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}\)