Beispiel Nr: 07
$c=\log_{b} a \Leftrightarrow b^{c}=a \quad \log_c a+\log_c b = \log_c (a \cdot b) \quad \log_c a-\log_c b =\log _c\frac{a}{b} \quad log_c a^n=n\log_c a \\ \\ \textbf{Gegeben:} \\ {a=3,43 \qquad b=3\frac{2}{5} \qquad c=4 \qquad n=5}\\ \\ \textbf{Rechnung:} \\ \log_{3\frac{2}{5}} 3,43 =1,01 \Leftrightarrow 3\frac{2}{5}^{1,01}=3,43 \\ \log_4 3,43+\log_4 3\frac{2}{5} = \log_4 (3,43 \cdot 3\frac{2}{5})= \log_4 (3,43 \cdot 3\frac{2}{5})=1,77 \\ \log_4 3,43-\log_4 3\frac{2}{5} =\log_4\frac{3,43}{3\frac{2}{5}}= 0,00718\\ \log_4 3,43^5=5\log_4 3,43 = 4,45\\ \log_3\frac{2}{5} 3,43=\dfrac{\log_4 3,43}{\log_4 3\frac{2}{5}}=1,01 $