# transform exponentials into logarithms

I was wondering if this:

$\exp( \ln(a) ) - \exp( \ln(0.1) + \ln(b) )$

Can be written using only logarithms as this:

$\ln(a)- \ln(0.1) - \ln(b)$

If this is wrong, is there a way to express the expression above using only logarithms?

Thank you.

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It should be : $$\exp(\ln(a))-\exp(\ln(0.1)+\ln(b))=\exp(\ln(a))-\exp(\ln(0.1b))=a-0.1b$$ Is this what you meant? So no logatrithms are even needed.
@Francesca If you must use logs, write it as $\ln\bigl(\exp(a-0.1b)\bigr)$. –  David Mitra Feb 4 '13 at 14:00
well you could also write the final answer $\ln(\exp(a-0.1b))$, but because the final answer is just $a-0.1b$ (so no logarithms at all) there is no 'natural' way without sort of forcing it to express your answer with just $\ln(a)$ and $\ln(b)$. –  Slugger Feb 4 '13 at 14:14