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logbase10(1/10) − logbase10(10/27) − logbase10 1000
I know all the rules for simplifying logs, however I cant seem to get this one right!
If any one could show me some working out towards the end of the simplification that would be great.
Thanks in advance for any help.
Mike
$\displaystyle log_{10}(0.1) = -1$Quote:
Originally Posted by mikewhant
$\displaystyle
log_{10}\left(\frac{10}{27}\right) = log_{10}(10) - 3log_{10}(3)$ (because $\displaystyle 27 = 3^3$)
$\displaystyle log_{10}(1000) = log_{10}(10^3) = 3$
So your sum reduces to $\displaystyle -1-(1-3log_{10}(3))-3 $
Thats great, just one further question, why is it + 3 on the end?
I can see now that log 1000 = 3, however in the original expression, it was
- log 1000, so should'nt it bee -3?
Thaanks again
Mike
Yes it should, that was an oversight on my part (Thinking)Quote:
Originally Posted by mikewhant
Thanks for pointing it out :)
Ah right ok, lol, funny because what was stumping me in the first place was the text book i have the question from gives the same answer you gave, + 3!
Anyway, thanks for that, all cleared up now!
Take care
Mike
