$\begin{array}{l} c=\log_{b} a \Leftrightarrow b^{c}=a \\ \log_c a+\log_c b = \log_c (a \cdot b) \\ \log_c a-\log_c b =\log _c\frac{a}{b} \\ log_c a^n=n\log_c a \\ \\ \textbf{Gegeben:} \\ {a=2 \qquad b=4 \qquad c=2 \qquad n=4}\\ \\ \textbf{Rechnung:} \\ \log_{4} 2 =\frac{1}{2} \Leftrightarrow 4^{\frac{1}{2}}=2 \\ \log_{2} 2+\log_{2}4 = \log_{2}(2 \cdot 4)= \log_{2}(2 \cdot 4)=3 \\ \log_{2} 2-\log_{2}4 =\log_{2}\frac{2}{4}= -1\\ \log_{2}2^4=4\log_{2}2 = 4\\ \log_{4} 2=\dfrac{\log_{2}2}{\log_{2}4}=\frac{1}{2} \end{array}$