a)
5^{x+2}-5^x=120
5^x*5^2-5^x=120
5^x(25-1)=120
5^x*24=120/:24
5^x=5^1
x=1
b)
(\frac{1}{2})^{x^2}*2^{2x+2}=\frac{1}{64}
2^{-x^2}*2^{2x+2}=(\frac{1}{2})^6
2^{-x^2+2x+2}=2^{-6}
-x^2+2x+2=-6
-x^2+2x+8=0
a=-1, b=2, c=8
\Delta=b^2-4ac=4-4*(-1)*8=4+32=36
\sqrt\Delta=6
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-2-6}{-2}=\frac{-8}{-2}=4
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-2+6}{-2}=\frac{4}{-2}=-2
c)
log_3(2x+1)=-1
3^{-1}=2x+1
\frac{1}{3}=2x+1
\frac{1}{3}-1=2x
-\frac{2}{3}=2x/:2
-\frac{\not2^1}{3}*\frac{1}{\not2^1}=x
-\frac{1}{3}=x
x=-\frac{1}{3}