anonymous
  • anonymous
How to write as a simple logarithm: log a + log (a+b) - log c - log d
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
The rules of logarithms are important here:\[\log(AB)=logA+logB\]\[\log(\frac{A}{B})=logA-logB\]
anonymous
  • anonymous
I got as far as log (((a^2)+ab)/(c/d))
anonymous
  • anonymous
but in the answer, the bottom of the equation is cd not c/d and I don't get why :(

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anonymous
  • anonymous
Working from that,\[\log a + \log (a+b) - \log c - \log d=\log(\frac{a(a+b)}{cd})\]
anonymous
  • anonymous
OK, this time step-by-step. From the product rule\[\log a + \log (a+b) - \log c - \log d=\log[a(a+b)]-\log c-\log d\]
anonymous
  • anonymous
ok following so far
anonymous
  • anonymous
Now, from the quotient rule\[\log[a(a+b)]−logc−logd=\log[\frac{a(a+b)}{c}]-logd\]
anonymous
  • anonymous
Apply the quotient rule again, to get\[\log[\frac{a(a+b)}{c}]−logd=\log[\frac{a(a+b)}{cd}]\]
anonymous
  • anonymous
Got it now?
anonymous
  • anonymous
and then with log d you do the same step as the last time!! Oh! How did you know to do the c first and then d though, I just did the first two parts with the multiplication law, and thelast two with the division law, and then both together with the division law
anonymous
  • anonymous
You eat an elephant one bite at a time. Do math the same way.
anonymous
  • anonymous
haha okay thanks so much :)
anonymous
  • anonymous
Do math every day.

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