Question 22, 4.3.13
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Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible.
\[
\ln \left(\frac{e^{7}}{17}\right)
\]
\[
\ln \left(\frac{e^{7}}{17}\right)=\square
\]
Answer
Final Answer: \( \boxed{4.166786655943784} \)
Step 1 ：The logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. Therefore, we can rewrite the expression as \( \ln(e^7) - \ln(17) \).
Step 2 ：The logarithm base e of e to the power of a number is just that number. Therefore, \( \ln(e^7) \) simplifies to 7.
Step 3 ：The final expression is \( 7 - \ln(17) \).
Step 4 ：Calculate the value of the expression to get the final answer.
Step 5 ：Final Answer: \( \boxed{4.166786655943784} \)
