[latex]log _{5}50 = log_{5}(25cdot{2}) = log_5{25}+log_5{2} = 2+log_{5}2[/latex] L=P [latex]log _{3}15 = log _{3}(5cdot{3}) = log_{3}3+log_{3}5 = 1+log_{3}5[/latex] L=P [latex]log _{4}6 + log _{4}8 = log_{4}(6cdot{8}) = log_{4}48[/latex] [latex]log_{4}48 = log_{4}(16cdot{3}) = log_{4}16+log_{4}3 = 2+log_{4}3[/latex] L=P [latex]log _{frac{1}{2}}5 - 1 = log_{frac{1}{2}}5-log_{frac{1}{2}}frac{1}{2} = log_{frac{1}{2}}(5:frac{1}{2}) = log_{frac{1}{2}}(5cdot{2}) = log_{frac{1}{2}}10[/latex] L=P --------------------------------------- Wykorzystane wzory: [latex]log_{a}b+log_{a}c = log_{a}(bcdot{c})[/latex] [latex]log_{a}b-log_{a}c = log_{a}(frac{b}{c})[/latex] [latex]1 = log_{a}a[/latex]
[latex] a)\ log _{5}50 = log_{5}(25cdot{2}) = log_5{25}+log_5{2} = 2+log_{5}2\ co nalezalo dowiesc \ \ b)\ log _{3}15 = log _{3}(5cdot{3}) = log_{3}3+log_{3}5 = 1+log_{3}5\ co nalezalo dowiesc\ [/latex] [latex] c)\ log _{4}6 + log _{4}8 = log_{4}(6cdot{8}) = log_{4}48=log_{4}(16cdot{3}) = \ =log_{4}16+log_{4}3 = 2+log_{4}3\ co nalezalo dowiesc\ \ d)\ log _{frac{1}{2}}5 - 1 = log_{frac{1}{2}}5-log_{frac{1}{2}}frac{1}{2} = log_{frac{1}{2}}(5:frac{1}{2}) = log_{frac{1}{2}}(5cdot{2}) = log_{frac{1}{2}}10\ co nalezalo dowiesc [/latex]
