Oblicz 1) [latex]log _{5} 16*log _{4} 27*log_{3}25[/latex] 2) [latex]log _{9} 16*log _{pierwiastekz2} 27[/latex]

1) [latex]log _{5} 16 cdot log _{4} 27 cdot log_{3}25=[/latex] [latex]frac{log16}{log5} cdot frac{log27}{log4} cdot frac{log25}{log3}=[/latex] [latex]frac{log2^4}{log5} cdot frac{log3^3}{log2^2} cdot frac{log5^2}{log3}=[/latex] [latex]frac{4log2}{log5} cdot frac{3log3}{2log2} cdot frac{2log5}{log3}=[/latex] [latex]frac{4}{1} cdot frac{3}{2} cdot frac{2}{1}=12[/latex] 2) [latex]log _{9} 16 cdot log _{ sqrt{2} } 27=[/latex] [latex]frac{log16}{log9} cdot frac{log27}{log sqrt{2} }=[/latex] [latex]frac{log2^4}{log3^2} cdot frac{log3^3}{log 2^{ frac{1}{2} }}=[/latex] [latex]frac{4log2}{2log3} cdot frac{3log3}{ frac{1}{2} log 2}=[/latex] [latex]frac{4}{2} cdot frac{3}{ frac{1}{2}}=12[/latex]