## Cutiepo0 3 years ago How to write as a simple logarithm: log a + log (a+b) - log c - log d

1. AnimalAin

The rules of logarithms are important here:$\log(AB)=logA+logB$$\log(\frac{A}{B})=logA-logB$

2. Cutiepo0

I got as far as log (((a^2)+ab)/(c/d))

3. Cutiepo0

but in the answer, the bottom of the equation is cd not c/d and I don't get why :(

4. AnimalAin

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

5. AnimalAin

OK, this time step-by-step. From the product rule$\log a + \log (a+b) - \log c - \log d=\log[a(a+b)]-\log c-\log d$

6. Cutiepo0

ok following so far

7. AnimalAin

Now, from the quotient rule$\log[a(a+b)]−logc−logd=\log[\frac{a(a+b)}{c}]-logd$

8. AnimalAin

Apply the quotient rule again, to get$\log[\frac{a(a+b)}{c}]−logd=\log[\frac{a(a+b)}{cd}]$

9. AnimalAin

Got it now?

10. Cutiepo0

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

11. AnimalAin

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

12. Cutiepo0

haha okay thanks so much :)

13. AnimalAin

Do math every day.