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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 :(

Working from that,\[\log a + \log (a+b) - \log c - \log d=\log(\frac{a(a+b)}{cd})\]

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?

You eat an elephant one bite at a time. Do math the same way.

haha okay thanks so much :)

Do math every day.