Question

How do you evaluate `f(x)=2lnx` for `x=0.75`?

Answer 1

With a calculator. And `f(0.75)~~-.5754`

Explanation:

You can do all sorts of things to this expression, but nothing will get you closer to an answer without using a calculator.
For example, on the right side, you have a rule of logarithms that says you can move that `2` in front of the natural log sign to the place of an exponent of the `x`:
`2ln 0.75= ln 0.75^2`.

You can rewrite `y= ln 0.75^2` as `e^y=0.75^2`, but this still gets you no closer to getting an answer.

So, plug it in your calculator. And if you don't understand what `e` is, or what logarithms are, check out videos about logarithms on Khan Academy and Eddie Woo's [video] on `e`.
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