Oblicz: a) log_{0,24}0,125 b) log_{125}0,2
a) log_{0,25}0,125=x\\ 0,25^x=0,125\\0,5^{2x}=0,5^3\\ 2x=3 \ |:2\\ x=\frac{3}{2}\\ x=1,5\\ log_{0,25}125=1,5
b) log_{125}0,2=x\\ 125^x=0,2\\ 5^{3x}=\frac{1}{5}\\ 5^{3x}=5^{-1}\\ 3x=-1 \ |:3 \\ x=-\frac{1}{3}\\ log_{125}0,2=-\frac{1}{3}