## anonymous 5 years ago condense this to a single quantity: 1/2lnX +ln(x+3)-ln(x^2 +1) thanks.

1. Owlfred

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2. anonymous

This appears to become a quadratic equation

3. anonymous

really? well im not sure because its logarithms and u need to condense it.

4. anonymous

how did you get that?

5. anonymous

well it is wrong, so don't write it!

6. anonymous

7. anonymous

oh i see could you please explain it to me?

8. anonymous

$\frac{1}{2}\ln(x)=\ln(\sqrt{x})$

9. anonymous

because $\ln(x^n)=n\ln(x)$

10. anonymous

here i am going from the right hand side to the left hand side.

11. anonymous

$\frac{1}{2}\ln(x)=\ln(x^{\frac{1}{2}})=\ln(\sqrt{x})$

12. anonymous

then we use $\ln(ab) = \ln(a)+ln(b)$ again from the right to the left.

13. anonymous

so we get $\ln(\sqrt{x})+\ln(x+3)=\ln(\sqrt{x}(x+3))$

14. anonymous

then we use $\ln(a)-\ln(b)=\ln(\frac{a}{b})$

15. anonymous

to get $\ln(\sqrt{x}(x+3))-\ln(x^2+1)=\ln(\frac{\sqrt{x}(x+3)}{x^2+1})$

16. anonymous

i made a mistake on the first try and wrote $\frac{1}{2}\ln(x)=\ln(x^2)$ which is wrong

17. anonymous

there now i deleted it. hope the steps are clear

18. anonymous

ohhh no i understand thanks so much!!:]

19. anonymous

welcome!