Zad 1 Oblicz a) [latex]log _{frac{1}{16} }} 2[/latex] b) [latex]log x_{8} sqrt{2} [/latex] c) [latex]log _{9 sqrt{3} } frac{1}{3} [/latex]

[latex]log_{a}b=c --- extgreater a^c=b\ \ a) (frac{1}{16})^x=2\ (2^{-4})^x=2^1\ 2^{-4x}=2^1\ -4x=1\ x=-frac{1}{4}\ \ b) log _{8} sqrt{2}=x\ 8^x=sqrt{2}\ (2^3)^x=2^{frac{1}{2}}\ 3x=frac{1}{2}\ x=frac{1}{6}\ \ c) log _{9 sqrt{3} } frac{1}{3} =x\ (9sqrt{3})^x=frac{1}{3}\ (3^2cdot 3^{frac{1}{2}})^x=3^{-1}\ (3^{frac{5}{2}})^x=3^{-1}\ frac{5}{2}x=-1\ x=-frac{2}{5} [/latex]