Đáp án:
\(x = {\log _{\frac{5}{3}}}\frac{{8 + \sqrt {89} }}{5}\)
Giải thích các bước giải:
\(\begin{array}{l}
{5.25^x} - {16.15^x} - {9^x}.5 = 0\\
\Leftrightarrow {5.5^{2x}} - {16.5^x}{.3^x} - {5.3^{2x}} = 0\\
\Leftrightarrow 5.{\left( {\frac{5}{3}} \right)^{2x}} - 16.{\left( {\frac{5}{3}} \right)^x} - 5 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{\left( {\frac{5}{3}} \right)^x} = \frac{{8 - \sqrt {89} }}{5}\,\,\,\left( {ktm} \right)\\
{\left( {\frac{5}{3}} \right)^x} = \frac{{8 + \sqrt {89} }}{5}\,\,\,\left( {tm} \right)
\end{array} \right.\\
\Leftrightarrow x = {\log _{\frac{5}{3}}}\frac{{8 + \sqrt {89} }}{5}.
\end{array}\)
