Zadanie 1
\frac{(a^{-3}*a^4)^4:a^{-7}}{a^{-5}:(a^3:a^{10})}=\frac{(a^{-3+4})^4:a^{-7}}{a^{-5}:a^{3-10}}=
=\frac{a^{4-(-7)}}{a^{-5-(-7)}}=\frac{a^{4+7}}{a^{-5+7}}=\frac{a^{11}}{a^2}=a^{11-2}=a^9
Zadanie 2
Porównaj liczby:
8^{20}=(2^3)^{20}=2^{60}
4^{30}=(2^2)^{30}=2^{60}
8^{20}=4^{30}
Zadanie 3
Oblicz:
a)
log_5\frac{1}{5}-log_{\sqrt3}9+\frac{1}{3}log_416^3=
=log_55^{-1}-log_{\sqrt3}3^2+log_4(16^3)^{\frac{1}{3}}=
-1-log_{\sqrt3}[(\sqrt3)^2]^2+log_416=
=-1-log_{\sqrt3}(\sqrt3)^4+log_44^2=
=-1-4+2=-3
b)
log8-3log2=log8-log2^3=log8-log8=0