Evaluate $\ln (0.396)$. Give your answer to 4 decimal places.
$\ln (0.396) =$
Answer (1)
Evaluate the natural logarithm of 0.396: ln ( 0.396 ) .
Use a calculator to find the natural logarithm: ln ( 0.396 ) ≈ − 0.9263410677 .
Round the result to 4 decimal places: − 0.9263 .
The natural logarithm of 0.396, rounded to 4 decimal places, is − 0.9263 .
Explanation
Problem Analysis We are asked to evaluate the natural logarithm of 0.396 and round the result to 4 decimal places. The natural logarithm, denoted as ln ( x ) , is the logarithm to the base e , where e ≈ 2.71828 .
Calculating the Natural Logarithm Using a calculator, we find that ln ( 0.396 ) ≈ − 0.9263410677 .
Rounding to 4 Decimal Places Rounding the result to 4 decimal places, we get − 0.9263 .
Final Answer Therefore, ln ( 0.396 ) ≈ − 0.9263 .
Examples
Natural logarithms are used in various fields such as physics, engineering, and finance. For example, in radioactive decay, the amount of a substance remaining after a certain time is modeled using an exponential function involving the natural logarithm. Similarly, in finance, continuously compounded interest is calculated using the natural logarithm. Understanding how to evaluate natural logarithms is essential for solving problems in these areas.
