a)
2^{x^2}=2
2^{x^2}=2^1
x^2=1
x^2-1=0
x^2-1^2=0 …wzór skróconego mnożenia a^2-b^2=(a-b)(a+b)
(x-1)(x+1)=0
x-1=0\vee x+1=0
x=1\vee x=-1 …\vee znaczy “lub”
b)
3^{x^2}=81
3^{x^2}=3^4
x^2=4
x^2-4=0
x^2-2^2=0
x=2\vee x=-2
c)
(\frac{1}{2})^{x^2-1}=0,5
\frac{1}{2})^{x^2-1}=(\frac{1}{2})^1
x^2-1=1
x^2-1-1=0
x^2-2=0
x^2-(\sqrt2)^2=0
(x-\sqrt2)(x+\sqrt2)=0
x=2\sqrt2 \vee x=-\sqrt2
d)
2^{x-1} = 4
2^{x-1}=2^2
x-1=2
x=2+1
x=3
e)
3^{x+4} = 27
3^{x+4}=3^3
x+4=3
x=3-4
x=-1