ln(1.032)/ln(0.9573)

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asked by guest
on Sep 20, 2024 at 1:57 am



You asked:

Evaluate the expression: \(\frac{\ln\left( 1.032 \right)}{\ln\left( 0.9573 \right)}\)

MathBot Answer:

\[\frac{\ln\left( 1.032 \right)}{\ln\left( 0.9573 \right)} = \frac{\log{\left(\frac{129}{125} \right)}}{\log{\left(\frac{9573}{10000} \right)}} \approx -0.72180982562787999627066168190536\]

\[\begin{aligned}\frac{\ln\left( 1.032 \right)}{\ln\left( 0.9573 \right)}& = \log{\left(1 + \frac{32}{1000} \right)} \cdot \frac{1}{\log{\left(\frac{9573}{10000} \right)}}\\& = \log{\left(1 + \frac{4}{125} \right)} \cdot \frac{1}{\log{\left(\frac{9573}{10000} \right)}}\\& = \log{\left(\frac{129}{125} \right)} \cdot \frac{1}{\log{\left(\frac{9573}{10000} \right)}}\\& = \frac{1}{\log{\left(\frac{9573}{10000} \right)}} \cdot \log{\left(\frac{129}{125} \right)}\end{aligned}\]

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