wzory: [latex]a^{log_ab}=b[/latex] [latex]log_{a^n}b= frac{1}{n} log_ab[/latex] a) [latex]4^{log_{4}3}=3[/latex] [latex]17^{2log_{17}40}=17^{log_{17}40^2}=40^2=1600[/latex] [latex]7^{log_{49}5-1}=7^{log_{49}5} cdot 7^{-1}=7^{log_{7^2}5} cdot frac{1}{7}=7^{ frac{1}{2} log_{7}5} cdot frac{1}{7}=7^{log_{7}5^{frac{1}{2}}} cdot frac{1}{7}= frac{ sqrt{5} }{7}[/latex] b) [latex]log_{sqrt{6}}3 cdot log_{3}36= frac{log3}{log sqrt{6} } cdot frac{log36}{log3}= frac{log6^2}{log6^{ frac{1}{2} }}=frac{2log6}{ frac{1}{2}log6}=4[/latex] [latex]log_{9}5 cdot log_{25}27= frac{log5}{log9} cdot frac{log27}{log25}=frac{log5}{log3^2} cdot frac{log3^3}{log5^2}=frac{log5}{2log3} cdot frac{3log3}{2log5}= frac{3}{4}[/latex] c) [latex]log_{12}2=a[/latex] [latex]log_{6}16= frac{log_{12}16}{log_{12}6}=frac{log_{12}2^4}{log_{12} frac{12}{2} }=frac{4log_{12}2}{log_{12}12-log_{12}2}= frac{4a}{1-a}[/latex]
