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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!)

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I would write $-\ln 4$ simply because it is typographically simplest -- it needs neither superscripts nor fractions -- and not obviously harder to understand than the others.

(But I would at least consider whether $-2\ln 2$ would be a more useful representation for the context).

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  • $\begingroup$ -2ln2 would be better - I agree. It was a poorly thought out example by myself. Thanks for pointing that out :) $\endgroup$ – iblamefish Aug 10 '13 at 15:57
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I don't believe there is a standard, though I haven't seen the last form before. Both of the first two look fine, though.

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