Question

evaluate the expression using a calculator.
\\(\frac{\ln 5}{4 \ln \left(1 + \frac{0.02}{4}\
ight)}\\)
\\(\frac{\ln 5}{4 \ln \left(1 + \frac{0.02}{4}\
ight)} \approx \square\\)
(do not round until the final answer. then round to four decimal places as needed.)

Explanation:

Step1: Calculate the denominator

First, calculate \(1+\frac{0.02}{4}=1 + 0.005=1.005\).
Then, find \(\ln(1.005)\approx0.0049875\).
Multiply by \(4\): \(4\ln(1.005)\approx4\times0.0049875 = 0.01995\).

Step2: Calculate the numerator

Find \(\ln(5)\approx1.6094379\).

Step3: Calculate the final value

Divide the numerator by the denominator: \(\frac{\ln(5)}{4\ln(1 + \frac{0.02}{4})}\approx\frac{1.6094379}{0.01995}\approx80.6736\).

Answer:

\(80.6736\)