Zadanie 1
a)
(\frac{1}{3})^{1-x}=(\frac{1}{81})^{x+1}
(\frac{1}{3})^{1-x}=(\frac{1}{3})^{4(x+1)}
1-x=4(x+1)
1-x=4x+4
-x-4x=4-1
-5x=3
x=-\frac{3}{5}
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2^{x-1}=\frac{1}{4}
2^{x-1}=(\frac{1}{2})^2
2^{x-1}=2^{-2}
x-1=-2
x=-2+1
x=-1
b)
3^{x-4}*27^{2-x}=9^{2x-3}
3^{x-4}*3^{3(2-x)}=3^{2(2x-3)}
3^{x-4+3(2-x)}=3^{4x-6}
3^{x-4+6-3x=3^{4x-6}}
3^{2-2x}=3^{4x-6}
2-2x=4x-6
-2x-4x=-6-2
-6x=-8
x=\frac{-8}{-6}=\frac{4}{3}
x=1\frac{1}{3}
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2^{x-4}*8^{3-2x}=4^{3x-3}
2^{x-4}*2^{3(3-2x)}=2^{2(3x-3)}
2^{x-4+3(3-2x)}=2^{6x-6}
2^{x-4+9-6x}=2^{6x-6}
2^{5-5x}=2^{6x-6}
5-5x=6x-6
-5x-6x=-6-5
-11x=-11 /:(-11)
x=1