Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
m,\\
4.{\left( {2x - 5} \right)^{100}} = 9.{\left( {5 - 2x} \right)^{98}}\\
\Leftrightarrow 4.{\left( {2x - 5} \right)^{100}} = 9.{\left( {2x - 5} \right)^{98}}\\
\Leftrightarrow 4.{\left( {2x - 5} \right)^{100}} - 9.{\left( {2x - 5} \right)^{98}} = 0\\
\Leftrightarrow {\left( {2x - 5} \right)^{98}}.\left[ {4.{{\left( {2x - 5} \right)}^2} - 9} \right] = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{\left( {2x - 5} \right)^{98}} = 0\\
4.{\left( {2x - 5} \right)^2} - 9 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x - 5 = 0\\
{\left( {2x - 5} \right)^2} = \dfrac{9}{4}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{5}{2}\\
2x - 5 = \dfrac{3}{2}\\
2x - 5 = - \dfrac{3}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{5}{2}\\
x = \dfrac{{13}}{4}\\
x = \dfrac{7}{4}
\end{array} \right.\\
n,\\
{7.5^{x + 1}} - {5^{x + 2}} - {2.10^2} = 50\\
\Leftrightarrow {7.5^{x + 1}} - {5.5^{x + 1}} - 2.100 = 50\\
\Leftrightarrow {5^{x + 1}}.\left( {7 - 5} \right) = 250\\
\Leftrightarrow {2.5^{x + 1}} = 250\\
\Leftrightarrow {5^{x + 1}} = 125\\
\Leftrightarrow {5^{x + 1}} = {5^3}\\
\Leftrightarrow x + 1 = 3\\
\Leftrightarrow x = 2
\end{array}\)
