\(A = 230\cdot \frac{1,021^{n}-1}{0,021} \big| \colon 230 \)
\(\frac{A}{230} = \frac{1,021^{n}-1}{0,021} \big| \cdot 0,021\)
\( \frac{A}{230} \cdot 0,021 = 1,021^{n} -1 \big| +1\)
\( \frac{A}{230} \cdot 0,021 + 1 = 1,021^{n} \big| log() \)
\( log(\frac{A \cdot 0,021}{230} + 1) = log(1,021^{n}) \dots \) Rechenregeln für Logarithmus
\( log(\frac{A \cdot 0,021}{230} + 1) = n \cdot log(1,021) \big| \colon log(1,021)\)
\( n = \frac{ log(\frac{A \cdot 0,021}{230} + 1)}{log(1,021)}\)
Anmerkungen zu den Rechenregeln (Exponentenregel):
\( log(a^{b}) = b \cdot log(a)\)
