Đáp án:
$\begin{array}{l}
a){\left( {4x - 5} \right)^2} + 34 = 70\\
\Leftrightarrow {\left( {4x - 5} \right)^2} = 36\\
\Leftrightarrow \left[ \begin{array}{l}
4x - 5 = 6\\
4x - 5 = - 6
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{11}}{4}\\
x = \dfrac{{ - 1}}{4}
\end{array} \right.\\
Vậy\,x = - \dfrac{1}{4};x = \dfrac{{11}}{4}\\
b){\left( {x - 13} \right)^{28}} - 9{\left( {x - 13} \right)^{26}} = 0\\
\Leftrightarrow {\left( {x - 13} \right)^{26}}.\left[ {{{\left( {x - 13} \right)}^2} - 9} \right] = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 13 = 0\\
x - 13 = 3\\
x - 13 = - 3
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 13\\
x = 16\\
x = 10
\end{array} \right.\\
Vậy\,x = 10;x = 13;x = 16\\
c){\left( {x + 17} \right)^{18}} = 25\left( {x + 7} \right)\\
\Leftrightarrow \left( {x + 7} \right).\left[ {{{\left( {x + 17} \right)}^{17}} - 25} \right] = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 7\\
{\left( {x + 17} \right)^{17}} = 25
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 7\\
x = - 17 + \sqrt[{17}]{{25}}
\end{array} \right.\\
d){5^{x - 3}} + {5^{x - 4}} = 150\\
\Leftrightarrow {5^{x - 4}}.\left( {5 + 1} \right) = 150\\
\Leftrightarrow {5^{x - 4}} = 25\\
\Leftrightarrow x - 4 = 2\\
\Leftrightarrow x = 6\\
Vậy\,x = 6\\
e){25^{x - 4}} = {125^6}\\
\Leftrightarrow {\left( {{5^2}} \right)^{x - 4}} = {\left( {{5^3}} \right)^6}\\
\Leftrightarrow 2\left( {x - 4} \right) = 3.6\\
\Leftrightarrow x - 4 = 9\\
\Leftrightarrow x = 13\\
Vậy\,x = 13
\end{array}$
