Hubungan Eksponen dan Logaritma
\(^a\log b = c \rightarrow a^c = b\)
\(a > 0, \: b > 0\) dan \(a \neq 1\)
Contoh 01
Tentukan nilai x dari:
\(^2 \log x = 3\)
\begin{equation*}
\begin{split}
& ^2 \log x = 3 \\\\
& x = 2^3 \\\\
& \bbox[5px, border: 2px solid magenta] {x = 8}
\end{split}
\end{equation*}
Sifat Logaritma 1
\(^a \log c^p = p \:.\: ^a \log c\)
\(^{a^q} \log c = \frac{1}{q} \:.\: ^a \log c\)
\(^{a^q} \log c^p = \frac{p}{q} \:.\: ^a \log c\)
Contoh 02
\begin{equation*}
\begin{split}
& ^7\log \frac{1}{49} \\\\
& ^7\log 7^{-2} \\\\
& -2 \:.\: ^7\log 7 \\\\
& \bbox[5px, border: 2px solid magenta] {-2}
\end{split}
\end{equation*}
Contoh 03
\begin{equation*}
\begin{split}
& ^8\log 2 \\\\
& ^{\large{2^3}}\log 2 \\\\
& \frac{1}{3}\:.\: ^2 \log 2 \\\\
& \bbox[5px, border: 2px solid magenta] {\frac{1}{3}}
\end{split}
\end{equation*}
Contoh 04
\begin{equation*}
\begin{split}
& ^{25}\log \frac{1}{625} \\\\
& ^{\large{5^2}}\log 5^{-4} \\\\
& \frac{-4}{2} \: .\: ^5 \log 5 \\\\
& \bbox[5px, border: 2px solid magenta] {-2}
\end{split}
\end{equation*}