Pomożecie ? Oblicz. [latex] 4log_{2} frac{1}{4} -3 * log_{5} sqrt{5} = ? [/latex] [latex] 8log frac{1}{10} -3 + 4log_{7}49 = ? [/latex] [latex] 5log_{6} 36 - 2 log frac{1}{100} = ? [/latex] [latex] 1500log_{7} 1 - 2000log_{50} 50 = ? [/latex]

[latex]4log_{2} frac{1}{4} -3 cdot log_{5} sqrt{5} =[/latex] [latex]4log_{2}left(frac{1}{2} ight)^2 -3 cdot log_{5} 5^{ frac{1}{2} } =[/latex] [latex]4log_{2}2^{-2} -3 cdot frac{1}{2} log_{5} 5 =[/latex] [latex]4 cdot (-2)log_{2}2 -3 cdot frac{1}{2} log_{5} 5 =[/latex] [latex]-8 cdot 1 -1,5 cdot 1 =-8-1,5=-9,5[/latex] ================ [latex]8log frac{1}{10} -3 + 4log_{7}49 =[/latex] [latex]8log10^{-1} -3 + 4log_{7}7^2 =[/latex] [latex]8 cdot (-1)log10 -3 + 4 cdot 2log_{7}7 =[/latex] [latex]-8 cdot 1 -3 + 8 cdot 1=-8-3+8=-3[/latex] ================ [latex]5log_{6} 36 - 2 log frac{1}{100} =[/latex] [latex]5log_{6} 6^2 - 2 log 10^{-2} =[/latex] [latex]5 cdot 2log_{6} 6 - 2 cdot (-2) log 10 =[/latex] [latex]10 cdot 1+4 cdot 1 =10+4=14[/latex] ================ [latex]1500log_{7} 1 - 2000log_{50} 50 =[/latex] [latex]1500 cdot 0 - 2000 cdot 1=0-2000=-2000[/latex]