Przyjmując, ze log6=0,8 oblicz a)log600 b)log0,06 c)log[latex] frac{50}{3} [/latex] d)[latex]6 sqrt{10} [/latex] e)log[latex]2 sqrt{15} [/latex]

[latex]\log600=log(6cdot10^2)=log6+log10^2=0,8+2=2,8 \ \log0,06=log dfrac{6}{10^2} =log6-log10^2=0,8-2=-1,2 \ \log dfrac{50}{3} =log dfrac{100}{6} =log10^2-log6=2-0,8=1,2 \ \log6 sqrt{10} =log6+ frac{1}{2} log10=0,8+0,5=1,3 \ \log2 sqrt{15} =log sqrt{4cdot15} =log sqrt{6cdot10} = dfrac{1}{2} (log6+log10)= \ \0,5cdot(0,8+1)=0,5cdot1,8=0,9[/latex]