Oblicz podstawę logarytmu a) [latex]log_a 81=4 [/latex] b) [latex]log_a 81=-4 [/latex] c) [latex]log_a9 =-2[/latex] d) [latex]log_a9 =1/2[/latex] e) [latex]log_a 8/125 =3[/latex] f) [latex]log_a 8/125 = -1[/latex]

[latex]log_a 81=4\ a^4=81\ a^4=3^4\ underline{a=3}[/latex] [latex]log_a 81=-4\ a^{-4}=81\ (frac{1}{a})^4=3^4\ frac{1}{a}=3\ underline{a=frac{1}{3}}[/latex] [latex]log_a 9=-2\ a^{-2}=9\ (frac{1}{a})^2=3^2\ frac{1}{a}=3\ underline{a=frac{1}{3}}[/latex] [latex]log_a 9=frac{1}{2}\ a^{frac{1}{2}}=9\ sqrt{a}=sqrt{9^2}\ sqrt{a}=sqrt{81}\ underline{a=81}[/latex] [latex]log_afrac{8}{125}=3\ a^3=frac{8}{125}\ a^3=(frac{2}{5})^3\ underline{a=frac{2}{5}}[/latex] [latex]log_a frac{8}{125}=-1\ a^{-1}=frac{8}{125}\ frac{1}{a}=frac{8}{125}\ a=frac{125}{8}\ underline{a=15frac{5}{8}}[/latex]