Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

v.s

  • 3 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]

  • This Question is Closed
  1. ghazi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  2. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    All of them are base e, surely?

  3. ghazi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oops my bad

  4. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  6. ghazi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  7. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  8. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  9. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i'm confused

  10. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  11. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  12. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  13. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or ln a - ln b =

  14. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ln(a/b)

  15. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes and ln a^2 =

  16. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2ln a

  17. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  18. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  19. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  20. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yess

  22. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so than how will be ?

  23. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  24. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  25. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  26. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  27. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you understand it sure ?

  29. v.s
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no

  30. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    are you here ?

  33. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  35. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you know ?

  36. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  37. jhonyy9
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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 ?

  38. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy