Question

evaluate the expression using a calculator.
\\(\frac{\ln 6}{8 \ln \left(1 + \frac{0.04}{8}\
ight)}\\)
\\(\frac{\ln 6}{8 \ln \left(1 + \frac{0.04}{8}\
ight)} \approx \square\\)
(do not round until the final answer. then round to four decimal places as needed.)

Explanation:

Step1: Calculate the value of $\ln6$

Using a calculator, $\ln6\approx1.791759469$

Step2: Calculate the value of $1+\frac{0.04}{8}$

$1+\frac{0.04}{8}=1 + 0.005=1.005$

Step3: Calculate the value of $\ln(1.005)$

Using a calculator, $\ln(1.005)\approx0.004987542$

Step4: Calculate the value of $8\ln(1.005)$

$8\times0.004987542 = 0.039900336$

Step5: Calculate the value of the fraction

$\frac{1.791759469}{0.039900336}\approx44.9060$

Answer:

$44.9060$