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

Sep 3, 2017

With a calculator. And $f \left(0.75\right) \approx - .5754$

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 $x$:
$2 \ln 0.75 = \ln {0.75}^{2}$.

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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