logarytmy. POMOCY 1. Liczbę [latex]{3log _2}3-{2log _2}5[/latex] można zapisać w postaci 2. Oblicz [latex]{log _ frac{1}{3} }3 sqrt{3}[/latex] 3. Oblicz [latex]{log _{2 sqrt{2}} } frac{1}{4}[/latex]

rozwiazanie w zalaczeniu............

1) [latex]3log_23-2log_25 = log_23^3-log_25^2 = log_2frac{3^3}{5^2} = log_2frac{27}{25}[/latex] 2) [latex]log_{frac{1}{3}}3 sqrt{3} = log_{frac{1}{3}}3^{frac{3}{2}} = log_{frac{1}{3}}(frac{1}{3})^{-frac{3}{2}} = -frac{3}{2} = -1,5[/latex] 3) [latex]log_{2 sqrt{2} }frac{1}{4} = log_{2^frac{3}{2}}(frac{1}{2})^2 = log_{2^frac{3}{2}}2^{-2} \ (2^{frac{3}{2}})^x = 2^{-2} \ frac{3x}{2} = -2 \ x = -frac{4}{3} \ log_{2^frac{3}{2}}2^{-2} = -frac{4}{3}[/latex]