$\begin{array}{l} c=\log_{b} a \Leftrightarrow b^{c}=a \\ \log_c a+\log_c b = \log_c (a \cdot b) \\ \log_c a-\log_c b =\log _c\frac{a}{b} \\ log_c a^n=n\log_c a \\ \\ \textbf{Gegeben:} \\ {a=5 \qquad b=8 \qquad c=3 \qquad n=2}\\ \\ \textbf{Rechnung:} \\ \log_{8} 5 =0,774 \Leftrightarrow 8^{0,774}=5 \\ \log_{3} 5+\log_{3}8 = \log_{3}(5 \cdot 8)= \log_{3}(5 \cdot 8)=3,36 \\ \log_{3} 5-\log_{3}8 =\log_{3}\frac{5}{8}= -0,428\\ \log_{3}5^2=2\log_{3}5 = 2,93\\ \log_{8} 5=\dfrac{\log_{3}5}{\log_{3}8}=0,774 \end{array}$