Bentuk \(a^{f(x)} = b \: ^{g(x)}\)
Solusi
Menambahkan \(\log\) pada kedua ruas.
\( \log a^{f(x)} = \log b \: ^{g(x)}\)
\( f(x) \:.\: \log a = g(x) \:.\: \log b \)
Contoh:
\(5^{x^2 + x - 2} = 3^{x + 2}\)
Solusi
\begin{equation*}
\begin{split}
& 5^{x^2 + x - 2} = 3^{x + 2} \\\\
& \log 5^{x^2 + x - 2} = \log 3^{x + 2} \\\\
& (x^2 + x - 2) \log 5 = (x + 2) \log 3 \\\\
& (x + 2)(x - 1) \log 5 - (x + 2) \log 3 = 0\\\\
& (x + 2)[(x - 1) \log 5 - \log 3] = 0
\end{split}
\end{equation*}
Faktor 1
\(x + 2 = 0 \)
\(x = -2 \)
Faktor 2
\((x - 1) \log 5 - \log 3 = 0 \)
\((x - 1) \log 5 = \log 3 \)
\(x - 1 = \dfrac{\log 3}{\log 5}\)
\({\color {blue} \dfrac{\log b}{\log a} = \log_a b}\)
\(x - 1 = \log_5 3 \)
\(x = 1 + \log_5 3 \)
\(x = \log_5 5 + \log_5 3 \)
\(x = \log_5 15\)
HP = \(\{-2, \log_5 15 \}\)