log(3)/log(1.06)
You asked:
Evaluate the expression: \(\frac{\log\left( 3 \right)}{\log\left( 1.06 \right)}\)
MathBot Answer:
\[\frac{\log\left( 3 \right)}{\log\left( 1.06 \right)} = \frac{\log{\left(3 \right)}}{\log{\left(\frac{53}{50} \right)}} \approx 18.85417667910729536417612821159456\]
\[\begin{aligned}\frac{\log\left( 3 \right)}{\log\left( 1.06 \right)}& = \log{\left(3 \right)} \cdot \frac{1}{\log{\left(1 + \frac{6}{100} \right)}}\\& = \log{\left(3 \right)} \cdot \frac{1}{\log{\left(1 + \frac{3}{50} \right)}}\\& = \log{\left(3 \right)} \cdot \frac{1}{\log{\left(\frac{53}{50} \right)}}\\& = \frac{1}{\log{\left(\frac{53}{50} \right)}} \cdot \log{\left(3 \right)}\end{aligned}\]