## animalsavior94 Group Title condense this to a single quantity: 1/2lnX +ln(x+3)-ln(x^2 +1) thanks. 3 years ago 3 years ago

1. Owlfred Group Title

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

2. LagrangeSon678 Group Title

This appears to become a quadratic equation

3. animalsavior94 Group Title

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

4. animalsavior94 Group Title

how did you get that?

5. satellite73 Group Title

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

6. satellite73 Group Title

7. animalsavior94 Group Title

oh i see could you please explain it to me?

8. satellite73 Group Title

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

9. satellite73 Group Title

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

10. satellite73 Group Title

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

11. satellite73 Group Title

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

12. satellite73 Group Title

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

13. satellite73 Group Title

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

14. satellite73 Group Title

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

15. satellite73 Group Title

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

16. satellite73 Group Title

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

17. satellite73 Group Title

there now i deleted it. hope the steps are clear

18. animalsavior94 Group Title

ohhh no i understand thanks so much!!:]

19. satellite73 Group Title

welcome!