Here is a general directive.
We can of course find Ln 2 by Taylor series
But how about Ln k where k is a positive integer.
Since we are dealing with Ln 3.5 as part of the problem here is a formula for k in
google search engine under" A Series for Ln k - JStor"
This gives a specimen page (one page only but containg the relevamt formula for k) by the
American Mathematical Monthly Vol. 105, No 6 (Jun - July 1998), pp 552-554
The entire article can be downloaded for $12.00
The formula will also give Ln 4
Ln 3.5 will lie between these two k's namely 3 and 4
Recall e^x is an ENTIRE FUNCTION and therefore its Maclaurin expansion is valid for ALL x .
Take the average value of Ln 3 and Ln 4
Expand this average value of Ln by the Maclaurin expansion for Exp x and see how close (after say about 4 or 5 terms of the Maclaurin Expansion) this is to the NUMBER 3.5.
This procedure is called a sequence of nested closed intervals rather like an iterative process.
A programme could be written for this fairly simple process.
Hope this helps