3 mark for review the function f is given by f(x)=ln x. which of the following describes input values for…

3 mark for review the function f is given by f(x)=ln x. which of the following describes input values for which the output values of f are integers? a integer powers of e b integer powers of 10 c integers raised to the power e d integers raised to the power 10

3 mark for review the function f is given by f(x)=ln x. which of the following describes input values for which the output values of f are integers? a integer powers of e b integer powers of 10 c integers raised to the power e d integers raised to the power 10

Answer

Explanation:

Step1: Recall the property of natural - logarithm

The natural - logarithm function is (y = \ln x=\log_{e}x). We want (y = n), where (n\in\mathbb{Z}).

Step2: Use the logarithmic - exponential conversion

If (\ln x=n), then by the definition of logarithms (x = e^{n}) (since if (y=\log_{a}x), then (x = a^{y}), here (a = e)). When (n) is an integer, (x) is an integer power of (e).

Answer:

A. Integer powers of (e)