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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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1 Answer

up vote 2 down vote accepted

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.

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Hi Teun, no I actually needed only logarithms… Can I then log this?a - 0.1b = ln(a) - 0.1*ln(b) ? –  Francesca Feb 4 '13 at 13:58
    
@Francesca If you must use logs, write it as $\ln\bigl(\exp(a-0.1b)\bigr)$. –  David Mitra Feb 4 '13 at 14:00
    
Hi David, thank you… I have only log(a) and log(b) and would like to express it as just these initial value, is this possible? –  Francesca Feb 4 '13 at 14:03
    
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
    
But forcing it to be expressed in terms of ln(a) and ln(b) is exactly what I would like to do… Is this impossible maybe? –  Francesca Feb 4 '13 at 14:17
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