Estimating the Natural Logarithm of 16
The question is asking for the best estimate of the natural logarithm of 16.
To estimate the value without a calculator, it helps to know the value of the natural logarithm for some key numbers. For example:
- ln(1) = 0
- ln(e) = 1, where e is approximately equal to 2.718
The value of ln(16) will be somewhere between the ln(e^2) and ln(e^3) since 16 is between e^2 and e^3. Knowing that:
- e^2 is approximately 7.389 (since 2.718 squared is about 7.389)
- e^3 is approximately 20.086 (since 2.718 cubed is about 20.086)
We can tell that ln(16) will be close to but less than 3 because 16 is less than e^3 but greater than e^2. Among the choices given, the best estimate for ln(16) which is just a bit under 3, would be:
C. 3.23
This is because 3.23 is the closest value under 3, which makes sense for an estimate of ln(16). It's a rough estimate, but it's the best fit given the options provided.
