\(5^{x^2 + x - 2} = 3^{x + 2}\)
\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
\((x - 1) \log 5 - \log 3 = 0 \)
\((x - 1) \log 5 = \log 3 \)
\(x - 1 = \dfrac{\log 3}{\log 5}\)
\({\color {blue} \dfrac{\log b}{\log a} = \: ^a \log b}\)
\(x - 1 = \: ^5 \log 3 \)
\(x = 1 + \: ^5 \log 3 \)
\(x = \: ^5 \log 5 + \: ^5 \log 3 \quad {\color {blue} \log a + \log b = \log (ab)}\)
\(x = \: ^5 \log 15\)
HP = \(\{-2, \: ^5 \log 15 \}\)