I.
1) log3 243 = x
[tex]3^{x}=243\\3^{x}=3^{5}\\x=5[/tex]
2) log1/2 32 = x
[tex]\frac{1}{2} ^{x} =32\\2^{-x}=2^{5}\\-x=5/*(-1)\\x=-5[/tex]
3) log1/6 216 = x
[tex]\frac{1}{6}^{x}=216\\ 6^{-x}=6^3\\-x=3\\x=-3[/tex]
4) log2 0,125 = x
[tex]2^{x}=0,125\\2^{x}=\frac{1}{8} \\2^{x}=2^{-3}\\x=-3[/tex]
5) log 0,001 = x
[tex]10^{x}=0,001\\10^{x}=\frac{1}{1000}\\10^{x}=10^{-3}\\x=-3[/tex]
6)log1/3 1 = x
[tex](\frac{1}{3}) ^{x}=1 \\x=0[/tex]
Bo każda liczba podniesiona do potęgi zerowej da nam 1
II.
1) log 25 + log 4 = log (25*4) = log 100 = 2
2) log 5000 - log 5 = log (5000/5) = log 1000 = 3
3) 4log 2 + 2log 25 = [tex]log2^{4}+log25^{2}=log 16 + log 625 = log (16*625)=log 10000 = 4[/tex]
