5/3.8^x+2-3/5.8^x=5/3.8^11-3/5.8^9 3/2.4^x+5/3.4^x+2=3/2.4^8+5/3.4^10

Đáp án:

$\begin{array}{l}
a)\\
\dfrac{5}{3}{.8^{x + 2}} - \dfrac{3}{5}{.8^x} = \dfrac{5}{3}{.8^{11}} - \dfrac{3}{5}{.8^9}\\
 \Leftrightarrow \dfrac{5}{3}{.8^x}{.8^2} - \dfrac{3}{5}{.8^x} = \dfrac{5}{3}{.8^9}{.8^2} - \dfrac{3}{5}{.8^9}\\
 \Leftrightarrow {8^x}.\left( {\dfrac{5}{3}{{.8}^2} - \dfrac{3}{5}} \right) = {8^9}.\left( {\dfrac{5}{3}{{.8}^2} - \dfrac{3}{5}} \right)\\
 \Leftrightarrow {8^x} = {8^9}\\
 \Leftrightarrow x = 9\\
Vậy\,x = 9\\
b)\\
\dfrac{3}{2}{.4^x} + \dfrac{5}{3}{.4^{x + 2}} = \dfrac{3}{2}{.4^8} + \dfrac{5}{3}{.4^{10}}\\
 \Leftrightarrow \dfrac{3}{2}{.4^x} + \dfrac{5}{3}{.4^x}{.4^2} = \dfrac{3}{2}{.4^8} + \dfrac{5}{3}{.4^8}{.4^2}\\
 \Leftrightarrow {4^x}.\left( {\dfrac{3}{2} + \dfrac{5}{3}{{.4}^2}} \right) = {4^8}.\left( {\dfrac{3}{2} + \dfrac{5}{3}{{.4}^2}} \right)\\
 \Leftrightarrow {4^x} = {4^8}\\
 \Leftrightarrow x = 8\\
Vậy\,x = 8
\end{array}$