## anonymous one year ago I have to write this as a single natural logarithm. 3 ln 3 + 2 ln x

1. Nnesha

same like log :=)

2. Nnesha

power rule first :=) it's like backwards :=)

3. Nnesha

power rule $\large\rm log_b x^y = y \log_b x$

4. anonymous

log3 3^2 = 2 log3 3 I am so bad at these

5. Nnesha

let's deal with log and ln today! so you can i'm really good at it!

6. anonymous

awesome okay

7. Nnesha

okay so here is an example ln and log same rules apply for both $\rm 5 \ln y = \ln y^5$ number at front of ln becomes exponent of y

8. Nnesha

|dw:1440780028325:dw|

9. Nnesha

so how would you write $\huge\rm 3 \ln 3 =??$ on the previous post you were expanding log equation not condense write in single ln form

10. anonymous

as ln^3?

11. anonymous

I'm sorry let me go back and try again thats wrong

12. Nnesha

okay :=)

13. anonymous

I feel like it should be ln 3^3

14. Nnesha

yes right!

15. Nnesha

same rules apply for 2 ln x = ??

16. anonymous

ln 2^2

17. Nnesha

hmm

18. Nnesha

there is only one 2

19. anonymous

oh right yeah

20. anonymous

so just ln 2 ?

21. Nnesha

it's 2 ln of x |dw:1440780554920:dw|

22. anonymous

oh okay

23. Nnesha

so 2 wll become exponent of x

24. anonymous

okay

25. Nnesha

so how would yo write 2 ln x = ?

26. anonymous

x^2 ?

27. Nnesha

yes right! but don't forget the ln so $\huge\rm \color{reD}{3} \ln 3 +\color{blue}{ 2} \ln x$$\huge\rm ln 3^\color{red}{2} + \ln x^\color{blue}{2}$ now we can write it in single ln

28. Nnesha

there is plus sign which property you should apply ?

29. anonymous

product rule?

30. Nnesha

yes right

31. anonymous

isnt this product rule logb(x ∙ y) = logb(x) + logb(y)

32. anonymous

so would all the logb be log3?

33. Nnesha

no simple log means log base 10

34. Nnesha

in ur question it's ln 3^3 + ln x^2

35. Nnesha

it's natural log you don't have to worry about the base

36. anonymous

so just ln 9x^2 ? I think

37. Nnesha

yes right

38. anonymous

oh well the last part was easier than I thought. i think I just get confused with how to simplify everything. Thank you I really appreciate you helping :)))

39. Nnesha

my pleasure :=)