Đáp án:
\(\left[ \begin{array}{l}
x = 0\\
x = {\log _3}4
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
x{\log _5}3 + {\log _5}\left( {{3^x} - 2} \right) = {\log _5}\left( {{3^{x + 1}} - 4} \right)\\
\Leftrightarrow {\log _5}{3^x} + {\log _5}\left( {{3^x} - 2} \right) = {\log _5}\left( {{{3.3}^x} - 4} \right)\\
\Leftrightarrow {\log _5}\left[ {{3^x}\left( {{3^x} - 2} \right)} \right] = {\log _5}\left( {{{3.3}^x} - 4} \right)\\
\Leftrightarrow {3^x}\left( {{3^x} - 2} \right) = {3.3^x} - 4\\
\Leftrightarrow {3^{2x}} - {2.3^x} - {3.3^x} + 4 = 0\\
\Leftrightarrow {3^{2x}} - {5.3^x} + 4 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{3^x} = 1\\
{3^x} = 4
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = {\log _3}4
\end{array} \right..
\end{array}\)
