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How to write as a simple logarithm: log a + log (a+b) - log c - log d

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

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Working from that,\[\log a + \log (a+b) - \log c - \log d=\log(\frac{a(a+b)}{cd})\]
OK, this time step-by-step. From the product rule\[\log a + \log (a+b) - \log c - \log d=\log[a(a+b)]-\log c-\log d\]
ok following so far
Now, from the quotient rule\[\log[a(a+b)]−logc−logd=\log[\frac{a(a+b)}{c}]-logd\]
Apply the quotient rule again, to get\[\log[\frac{a(a+b)}{c}]−logd=\log[\frac{a(a+b)}{cd}]\]
Got it now?
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
You eat an elephant one bite at a time. Do math the same way.
haha okay thanks so much :)
Do math every day.

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