Persamaan Logaritma
Fungsi yang sama
\(^a \log f(x) = \: ^b \log f(x) \)
\(f(x) = 1 \) atau \(a = b\)
Contoh
\(^2 \log (x^2 - x + 1) = \: ^5 \log (x^2 - x + 1)\)
\begin{equation*} \begin{split} & x^2 - x + 1 = 1 \\\\ & x^2 - x = 0 \\\\ & x \:.\: (x - 1) = 0\\\\ & \bbox[5px, border: 2px solid magenta] {x = 0 \text{ atau } x = 1} \end{split} \end{equation*}
HP = {0, 1}
Basis yang sama
\(^a \log f(x) = \: ^a \log g(x) \)
\(\cancel {^a \log} f(x) = \: \cancel {^a \log} g(x) \)
\(f(x) = g(x) \)
Syarat basis
\(a > 0\) dan \(a \neq 1\)
Syarat terdefinisi
\(f(x_1) > 0\) dan \(g(x_1) > 0\)
Contoh
\(^3 \log(x - 4) = 1\)
\begin{equation*} \begin{split} & ^3 \log(x - 4) = 1 \\\\ & \cancel {^3 \log} (x - 4) = \cancel {^3 \log} 3 \\\\ & x - 4 = 3 \\\\ & \bbox[5px, border: 2px solid magenta] {x = 7} \end{split} \end{equation*}
Syarat terdefinisi
\begin{equation*} x - 4 = 7 - 4 \: {\color {blue} > 0 \quad \text{ OK!}} \end{equation*}
HP = {7}
Bentuk Yang Dapat Difaktorkan
\(A(^a \log x)^2 + B(^a \log x) + C = 0 \)
Contoh
\(^3 \log^2 x - \: ^3 \log x = 0\)
SOAL LATIHAN