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anonymous

  • one year ago

I have to write this as a single natural logarithm. 3 ln 3 + 2 ln x

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  1. Nnesha
    • one year ago
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    same like log :=)

  2. Nnesha
    • one year ago
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    power rule first :=) it's like backwards :=)

  3. Nnesha
    • one year ago
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    power rule \[\large\rm log_b x^y = y \log_b x\]

  4. anonymous
    • one year ago
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    log3 3^2 = 2 log3 3 I am so bad at these

  5. Nnesha
    • one year ago
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    let's deal with log and ln today! so you can i'm really good at it!

  6. anonymous
    • one year ago
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    awesome okay

  7. Nnesha
    • one year ago
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    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
    • one year ago
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    |dw:1440780028325:dw|

  9. Nnesha
    • one year ago
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    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
    • one year ago
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    as ln^3?

  11. anonymous
    • one year ago
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    I'm sorry let me go back and try again thats wrong

  12. Nnesha
    • one year ago
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    okay :=)

  13. anonymous
    • one year ago
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    I feel like it should be ln 3^3

  14. Nnesha
    • one year ago
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    yes right!

  15. Nnesha
    • one year ago
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    same rules apply for 2 ln x = ??

  16. anonymous
    • one year ago
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    ln 2^2

  17. Nnesha
    • one year ago
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    hmm

  18. Nnesha
    • one year ago
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    there is only one `2`

  19. anonymous
    • one year ago
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    oh right yeah

  20. anonymous
    • one year ago
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    so just ln 2 ?

  21. Nnesha
    • one year ago
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    it's 2 ln of x |dw:1440780554920:dw|

  22. anonymous
    • one year ago
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    oh okay

  23. Nnesha
    • one year ago
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    so 2 wll become exponent of x

  24. anonymous
    • one year ago
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    okay

  25. Nnesha
    • one year ago
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    so how would yo write 2 ln x = ?

  26. anonymous
    • one year ago
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    x^2 ?

  27. Nnesha
    • one year ago
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    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
    • one year ago
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    there is plus sign which property you should apply ?

  29. anonymous
    • one year ago
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    product rule?

  30. Nnesha
    • one year ago
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    yes right

  31. anonymous
    • one year ago
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    isnt this product rule logb(x ∙ y) = logb(x) + logb(y)

  32. anonymous
    • one year ago
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    so would all the logb be log3?

  33. Nnesha
    • one year ago
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    no simple log means log base 10

  34. Nnesha
    • one year ago
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    in ur question it's ln 3^3 + ln x^2

  35. Nnesha
    • one year ago
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    it's natural log you don't have to worry about the base

  36. anonymous
    • one year ago
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    so just ln 9x^2 ? I think

  37. Nnesha
    • one year ago
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    yes right

  38. anonymous
    • one year ago
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    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
    • one year ago
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    my pleasure :=)

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