Question

Are `lne` and `lne^x` the same?

Answer 1

No

Explanation:

As `ln` is the natural logarithm then is is a logarithm using base `e` and therefore we can directly evaluate the two expressions as:

`ln e \ \= 1`
`ln e^x = x`

These are clearly not the same.

If we could not directly evaluate then we can use the fact that for any base `b` then:

`log_b A = log_b B iff A=B`

and again it is clear that `e` and `e^x` are not identical.