a)
(0,4)^x=6,25
(\frac{4}{10})^x=\frac{625}{100}
(\frac{2}{5})^x=\frac{25}{4}
(\frac{2}{5})^x=(\frac{5}{2})^2
(\frac{2}{5})^x=(\frac{2}{5})^{-2}
x=-2
b)
(\frac{3}{4})^{x+5}=(\frac{4}{3})^{x+1}
(\frac{3}{4})^{x+5}=(\frac{3}{4})^{-(x+1)}
x+5=-(x+1)
x+5=-x-1
x+x=-1-5
2x=-6 |:2
x=-3
c)
(\frac{1}{2})^{x^2-2x}=32^{x-2}
(\frac{1}{2})^{x^2-2x}=2^{5(x-2)}
(\frac{1}{2})^{x^2-2x}=(\frac{1}{2})^{-5(x-2)}
x^2-2x=-5(x-2)
x^2-2x=-5x+10
x^2-2x+5x-10=0
x^2+3x-10=0
\Delta=9-4*(-10)=49
\sqrt\Delta=7
x_1=\frac{-3-7}{2}=-5
x_2=\frac{-3+7}{2}=2