a) [latex]a^{x}:a^{y}=a^{x-y}[/latex] [latex]frac{a^{3}:a^{5}}{a^{-4}}=frac{a^{3-5}}{a^{-4}}=frac{a^{-2}}{a^{-4}}=a^{-2-(-4)}=a^{-2+4}=a^{2} [/latex] b) [latex]a^{-x}=(frac{1}{a})^{x}\a^{frac{x}{y}}=sqrt[y]{a^{x}}\\(2frac{1}{4})^{-frac{1}{2}}=(frac{9}{4})^{-frac{1}{2}}=(frac{4}{9})^{frac{1}{2}}=sqrt{frac{4}{9}}=frac{2}{3}[/latex] c) [latex]log_{a}b+log_{a}c=log_{a}(b*c)\log_{a}b=c iff a^{c}=b\\log_{12}frac{1}{9}+log_{12}frac{1}{16}=log_{12}(frac{1}{9}*frac{1}{16})=log_{12}frac{1}{144}=-2\\ o log_{12}frac{1}{144}=-2 bo 12^{-2}=(frac{1}{12})^{2}=frac{1}{144}[/latex] d) [latex]log_{a}b=c iff a^{c}=b\\log_{frac{1}{2}}4sqrt[3]{16}=x\\(frac{1}{2})^{x}=4sqrt[3]{16}\\(2^{-1})^{x}=2^{2}*(2^{4})^{frac{1}{3}}\2^{-x}=2^{2}*2^{frac{4}{3}}\2^{-x}=2^{2+frac{4}{3}}\2^{-x}=2^{3frac{1}{3}}\-x=3frac{1}{3} /:(-1)\x=-3frac{1}{3} o log_{frac{1}{2}}4sqrt[3]{16}=-3frac{1}{3}[/latex]
Zad 1: Oblicz a) [latex]log _{4} 2 [/latex] b) [latex]log _{4} 8[/latex] c) [latex]log _{4} frac{1}{1024} [/latex] d) [latex]log _{4} frac{1}{ sqrt{2} } [/latex] Proszę o pomoc, daję naj :)...
Oblicz: a) [latex]log frac{1}{3} 81 sqrt[4]{3}= [/latex] b) Wiedząc, że [latex]log 5^{2}= a [/latex] oblicz [latex]log _{5} frac{2}{25} [/latex] c) [latex][ (frac{2}{3}) ^{-1}-4 ^{-1}] ^{-1}= [/latex] d) [latex]( sqrt{3}- sqrt{2}) ^{2}= ...
Pilne.Oblicz. a.) [latex]log_{frac{1}{5}} 5sqrt{5}= [/latex] b.) [latex]log_{frac{4}{3}}(log_{4}2sqrt{2})=[/latex] c.) [latex]log_{36}6+log_{16}4-log_{8}2=[/latex] d.) [latex]frac{25}{5frac{3}{2}} =[/latex] e.) [latex]frac{3frac{3}{2}}{sqrt{3}}=[/la...
oblicz [latex]frac{sqrt{a*b^2}}{c}[/latex] jezeli [latex]log_{3}[/latex] a=5 , [latex]log_{2} [/latex] b=⅛ , [latex]log_{c}[/latex] 9=4...
1 Oblicz a. log 100 + log 4 [latex] frac{1}{16} [/latex] b. log [latex] 10^{7} [/latex] - log 0,5 8 c. log 6 [latex] frac{1}{36} [/latex] + log [latex] sqrt[3]{10} [/latex] d. log [latex] sqrt[4]{10} [/latex] - log 3 [latex] sqrt[4]{3} [/latex] ...
