proszę pomóżcie mi rozwiązac te 3 zadania w załączniku 

[latex]3.165\a) log_{0,1}0,01=log_{0,1}(0,1)^2=2log_{0,1}0,1=2\\b) log_{1,1}1,331=log_{1,1}(1,1)^3=3log_{1,1}1,1=3\\c) log_{0,64}0,8=log_{0,64}sqrt{0,8^2}=log_{0,64}sqrt{0,64}=log_{0,64}(0,64)^frac{1}{2}=frac{1}{2}\\d) log_{0,125}0,5=log_{0,125}sqrt[3]{0,5^3}=log_{0,125}0,125^frac{1}{3}=frac{1}{3}\\e) log_{0,16}0,064=log_{0,16}0,4^3=3log_{0,16}0,4=3log_{0,16}sqrt{0,4^2}\\=3log_{0,16}0,16^frac{1}{2}=3cdotfrac{1}{2}=frac{3}{2}[/latex] [latex]f) log_{0,2}625=log_{frac{1}{5}}5^4=4log_frac{1}{5}5=4log_frac{1}{5}(frac{1}{5})^{-1}=-1cdot4log_frac{1}{5}frac{1}{5}=-4[/latex] [latex]g) log_{0,0016}5=log_frac{16}{10000}5=log_frac{2^4}{10^4}5=log_{left(frac{2}{10} ight)^4}5=log_{left(frac{1}{5} ight)^4}5\\=log_{left(frac{1}{5} ight)^4}sqrt[4]{5^4}=log_{left(frac{1}{5} ight)^4}left(5^4 ight)^frac{1}{4}=frac{1}{4}log_{left(frac{1}{5} ight)^4}5^4=frac{1}{4}log_{left(frac{1}{5} ight)^4}left(frac{1}{5} ight)^{-4}\\=frac{1}{4}log_{left(frac{1}{5} ight)^4}left[left(frac{1}{5} ight)^4 ight]^{-1}=-frac{1}{4}[/latex] [latex]h) log_40,0625=log_4frac{625}{10000}=log_4frac{1}{16}=log_416^{-1}=-log_416\\=-log_44^2=-2[/latex] ============================================================ [latex]3.166\a) log_{sqrt5}5sqrt[3]5=log_{sqrt5}(5^1cdot5^frac{1}{3})=log_{sqrt5}5^frac{4}{3}=frac{4}{3}log_{sqrt5}5=frac{4}{3}log_{sqrt5}(sqrt{5})^2\\=2cdotfrac{4}{3}log_{sqrt5}sqrt5=frac{8}{3}\\b) log_{sqrt[3]3}27=log_{sqrt[3]3}3^3=3log_{sqrt[3]3}3=3log_{sqrt[3]3}(sqrt[3]3)^3}=3cdot3log_{sqrt[3]3}sqrt[3]3=9\\c) log_28sqrt2=log_2(2^3cdot2^frac{1}{2})=log_22^{3frac{1}{2}}=3frac{1}{2}[/latex] [latex]d) log_frac{1}{3}81sqrt3=log_frac{1}{3}(3^4cdot3^frac{1}{2})=log_frac{1}{3}3^{4frac{1}{2}}=4frac{1}{2}\\e) log_48sqrt[4]2=log_4(2^3cdot2^frac{1}{4})=log_42^{3frac{1}{4}}=3frac{1}{4}log_42=3frac{1}{4}log_4sqrt{2^2}\\=3frac{1}{4}log_44^frac{1}{2}=frac{1}{2}cdotfrac{13}{4}log_44=frac{13}{8}\\f) log_frac{1}{5}25sqrt5=log_frac{1}{5}(5^2cdot5^frac{1}{2})=log_frac{1}{5}5^{2frac{1}{2}}=2frac{1}{2}log_frac{1}{5}5=2frac{1}{2}log_frac{1}{5}(frac{1}{5})^{-1}\\=-2frac{1}{2}[/latex] [latex]g) log_{sqrt3}sqrt[3]9=log_{sqrt3}9^frac{1}{3}=frac{1}{3}log_{sqrt3}3^2=2cdotfrac{1}{3}log_{sqrt3}3=frac{2}{3}log_{sqrt3}(sqrt3)^2\\=2cdotfrac{2}{3}log_{sqrt3}{sqrt3}=frac{4}{3}\\h) log_{2sqrt2}4sqrt8=log_{sqrt{2^2cdot2}}4sqrt{2^3}=log_{sqrt{2^3}}(2^2cdot2^frac{3}{2})=log_{sqrt{2^3}}2^frac{7}{2}[/latex] [latex]=frac{7}{2}log_{sqrt{2^3}}2=frac{7}{2}log_{sqrt{2^3}}(2^3)^frac{1}{3}=frac{1}{3}cdotfrac{7}{2}log_{sqrt{2^3}}2^3=frac{7}{6}log_{sqrt{2^3}}(sqrt{2^3})^2\\=2cdotfrac{7}{6}log_{sqrt{2^3}}sqrt{2^3}=frac{7}{3}[/latex] =========================================================== [latex]3.167\Dziedzina do kazdego przykladu:xinmathbb{R^+}\\a) log_3x=-1iff x=3^{-1} o x=frac{1}{3}\\b) log_5x=3iff x=5^3 o x=125\\c) log_frac{1}{2}x=-2iff x=(-frac{1}{2})^{-2} o x=(-2)^2 o x=4\\d) log_frac{1}{3}x=-frac{1}{2}iff x=(frac{1}{3})^{-frac{1}{2}} o x=3^frac{1}{2} o x=sqrt3[/latex] [latex]e) log_2x=-frac{2}{3}iff x=2^{-frac{2}{3}} o x=(frac{1}{2})^frac{2}{3} o x=sqrt[3]{frac{1}{4}}\\ o x=frac{1}{sqrt[3]4}cdotfrac{sqrt[3]2}{sqrt[3]2} o x=frac{sqrt[3]2}{sqrt[3]8} o x=frac{sqrt[3]2}{2}\\f) log_4x=0iff x=4^0 o x=1\\g) log_2x=10iff x=2^{10} o x=1024\\h) log_{2sqrt2}x=-3iff x=(2sqrt2)^{-3} o x=(frac{1}{2sqrt2})^3\\ o x=frac{1}{8cdot2sqrt2} o x=frac{1}{16cdotsqrt2}cdotfrac{sqrt2}{sqrt2} o x=frac{sqrt2}{16cdot2} o x=frac{sqrt2}{32}[/latex]