a) $5^x.(5^3)^2=625\Leftrightarrow 5^x.5^6=5^4\Leftrightarrow 5^{x+6}=5^4 \Rightarrow x+6 =4 \Rightarrow x=-2 $.b) $\left(\frac{12}{25}\right)^x=\left(\frac{5}{3}\right)^{-2}-\left(\frac{-3}{5}\right)^4 $.
Ta có $VP=\left(\frac{3}{5}\right)^2-\left(\frac{3}{5}\right)^4=\left(\frac{3}{5}\right)^2.\left[1-\left(\frac{3}{5}\right)^2 \right] =\left(\frac{3}{5}\right)^2.\left(\frac{4}{5}\right)^2 =\left( \frac{12}{25}\right)^2$.
Suy ra $\left(\frac{12}{25}\right)^x =\left(\frac{12}{25} \right)^2$ suy ra $x=2$.
c) $\left(\frac{-3}{4}\right)^{3x-1}=\frac{256}{81} \Leftrightarrow \left(\frac{4}{-3}\right)^{1-3x}=\left(\frac{4}{-3}\right)^4$ suy ra $1-3x=4$ suy ra $x=-1$.