Zadanie 15
a)
((\frac{1}{2})^a)^2=\frac{1}{64}
(\frac{1}{2})^{2a}=(\frac{1}{2})^6
2a=6 |:2
a=3
b)
\frac{16^3}{2^b}=8
16^3=2^b*2^3
(2^4)^3=2^b*2^3
2^b=\frac{2^{12}}{2^3}
2^b=2^{12-3}
2^b=2^9
b=9
c)
64^2=c^6
(4^3)^2=c^6
4^6=c^6
4=c
c=4
d)
\frac{3^{10}}{27^d}=3
27^d=\frac{3^{10}}{3}
(3^3)^d=3^9
3^{3d}=3^9
3d=9 |:3
d=3
e)
\frac{125^e}{5^4}=5^5
125^e=5^4*5^5
(5^3)^e=5^9
5^{3e}=5^9
3e=9 |:3
e=3
f)
(81^2)^f:9=3^6
\frac{81^{2f}}{3^2}=3^6
81^{2f}=3^6*3^2
(3^4)^{2f}=3^8
3^{8f}=3^8
8f=8
f=1
Zadanie 18
II 2^{500}=(2^5)^{100}=32^{100}
IV 3^{400}=(3^4)^{100}=81^{100}
III 4^{300}=(4^3)^{100}=64^{100}
I 5^{200} =(5^2)^{100}=25^{100} najmniejsza