2:
a: \(3^{2x+6}=3^{10}\)
=>2x+6=10
=>2x=4
=>x=2
b: \(5^{x-1}=5^2\)
=>x-1=2
=>x=3
c: \(\left(-\dfrac{5}{9}\right)^{10}:x=\left(-\dfrac{5}{9}\right)^8\)
=>\(x=\left(-\dfrac{5}{9}\right)^{10}:\left(-\dfrac{5}{9}\right)^8=\left(-\dfrac{5}{9}\right)^2=\dfrac{25}{81}\)
d: \(x:\left(-\dfrac{5}{9}\right)^8=\left(-\dfrac{9}{5}\right)^8\)
=>\(x=\left(-\dfrac{9}{5}\right)^8\cdot\left(\dfrac{-5}{9}\right)^8=1\)
4:
a: \(\left(-\dfrac{8}{13}\right)^x=\dfrac{64}{169}\)
=>\(\left(-\dfrac{8}{13}\right)^x=\left(-\dfrac{8}{13}\right)^2\)
=>x=2
b: \(9^x:3^x=3\)
=>3^x=3
=>x=1
c: \(\left(x+0,8\right)^2=0,25\)
=>\(\left[{}\begin{matrix}x+0,8=0,5\\x+0,8=-0,5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-0,3\\x=-1,3\end{matrix}\right.\)
d: \(\left(x-\dfrac{1}{3}\right)^3=8\)
=>x-1/3=2
=>x=7/3