## v.s 2 years ago Express the given quantity as a single logarithm. 1/5 ln(x + 2)^5 + 1/2 [ln x − ln(x^2 + 3x + 2)^2]

1. ghazi

$\frac{ 1 }{ 5 }\log(x+2)^5+\frac{ 1 }{ 2 }[{\ln x- \ln (x^2+3x+2)^2}]= \frac{ 1 }{ 5 }*5 \log(x+2)+\frac{ 1 }{2 }[\ln x- \ln(x^2+3x+2)^2]$ i am sorry to say, this can't be unified because ln and log have different bases

2. henpen

All of them are base e, surely?

3. ghazi

4. henpen

Are there any nice identities for$\log(a)^b$? Maybe I'm being stupid.

5. henpen

Also- does anyone know how to have latex flow with your text rather than indent?

6. ghazi

no you are right ...and it can be simplified

7. jhonyy9

do you know the property of logarithm ? so like ln a + ln b = ? or ln a -ln b = ? or ln a^2 = ?

8. jhonyy9

you dont like cooperating nothing ? i like help you here ... come on !!!

9. v.s

i'm confused

10. jhonyy9

why ? so you know that ln a + ln b = ln a*b yes ?

11. v.s

yes

12. jhonyy9

so than do you know how many will be ln a^2 =

13. jhonyy9

or ln a - ln b =

14. v.s

ln(a/b)

15. jhonyy9

yes and ln a^2 =

16. v.s

2ln a

17. jhonyy9

yes right sure so than these property of logarithms can us in case of your exercise too ?

18. v.s

(ln(x + 2) (1/2 ln x / 2ln(x^2 + 3x + 2))

19. v.s

[ln(x + 2)] [1/2( ln x / 2ln(x^2 + 3x + 2))]

20. jhonyy9

so the first part is right but the secondly you need to separate 1/5 ln(x+2)^5 = 5/5 ln(x+2) = ln(x+2) this is right so in the second part there are 1/2 (ln x - ln(x^2 +3x +2)^2) = 1/2 (ln (x/(x^2 +3x +2)^2) = ln (x/(x^2 +3x +2)^2)^(1/2) do you understand till now ? can you continue it ?

21. v.s

yess

22. jhonyy9

so than how will be ?

23. v.s

[ln(x+2)] [ln (x/(x^2 +3x +2)^2)^(1/2)]

24. jhonyy9

why ? than you know that (a^2)^(1/2) =a^(2/2) =a so than what will be ?

25. jhonyy9

and you know that ln a +ln b = ln a*b

26. v.s

[ln(x+2)] [ln (x/(x^2 +3x +2)]

27. jhonyy9

not is right please check it because there is just (x^2 +3x +2)^2 and x on numerator have not exponent 2 so what sign that not can be simplified by 1/2 OK ?

28. jhonyy9

do you understand it sure ?

29. v.s

no

30. jhonyy9

so the first part is right sure will be ln(x+2) OK . in the second part there are 1/2 (ln x - ln(x^2 +3x +2)^2) = 1/2 (ln (x/(x^2 +3x +2)^2)) = ln (x^(1/2) /((x^2 +3x +2)^2)^1/2 = ln (x^1/2) /(x^2 +3x +2) so can you continue it now ?

31. jhonyy9

so than will result there ln (x+2) + ln (x^1/2) /(x^2 +3x +2) so from this can you continue it ?

32. jhonyy9

are you here ?

33. jhonyy9

so than will be using the property of logarithm log a +log b = log a*b so than will be ln ((x+2)*x^1/2 ) /(x^2 +3x +2)

34. jhonyy9

so x^2 +3x +2 how can you factoriz it ?

35. jhonyy9

do you know ?

36. jhonyy9

so x^2 +3x +2 = (x+2)(x+1) is right ?

37. jhonyy9

so than will be ln (x+2)x^(1/2) /(x+2)(x+1) so simplifie by (x+2) and will result ln x^1/2 /(x+1) so do you understand it now sure ?