I have been out of maths for around 10 years and I'm just getting back into it with a degree on the Open University. I have a question about simplifying expressions - and which representation is considered to be the most simple.
This might be completely subjective and context driven - but I'd like to know if there are any rules about this which I may have forgotten.
Say I am trying to simplify the expression:
$$\ln4 - 4\ln2 $$
I know that this simplifies to $$ \ln4 - 2\ln4 $$
which again simplifies to
$$-\ln4$$
I can think of three ways of representing this, and I'm not sure which is best:
$$ -\ln4 $$
$$ \ln\frac{1}{4} $$
$$ \ln(4^{-1}) $$
Is there a standard?
(Please forgive my terrible LaTeX skills, I'm just starting out!)