Wzór
a^{log_a x}=x
Rozwiązanie
A.
10^{log 17}=10^{log_{10}17}=17
B.
5^{1-log_5 3}=5^{log_55-log_5 3}=5^{log_5\frac{5}{3}}=\frac{5}{3}
C.
27^{log_3 2}=3^{3log_32}=3^{log_32^3}=3^{log_38}=8
D.
2^{1+log_4 5}=
=log\sqrt{4}^{log_44+log_45}
=log4^{\frac{1}{2}log_420}
=log4^{\frac{1}{2}log_4 \sqrt{20}}
=log4^{log_420^{\frac{1}{2}}}
=20^{\frac{1}{2}}=\sqrt{20}=\sqrt{4\cdot 5}=2\sqrt5