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How to distribute ln into right side of this equation

  1. Mar 3, 2012 #1
    ln.jpg



    once i get ln on both sides, i'm then supposed to differentiate both sides...but I won't be able to properly differentiate if ln is not applied.

    Does ln get applied to the 976, (-1) and 176t? How?
     
  2. jcsd
  3. Mar 3, 2012 #2
    You can use the chain rule here.

    Treat 976[ (.835)^t - 1] + 176t as a function of t. Then your equation becomes ln( f(t) ). And you can use the chain rule to determine the derivative.
     
  4. Mar 3, 2012 #3

    Mark44

    Staff: Mentor

    To answer the question in your title, you can't "distribute" ln into a sum, because ln is not a factor.

    Distributive property: a(b + c) = ab + ac

    BUT
    cos(b + c) ≠ cos(b) + cos(c)
    ln(b + c) ≠ ln(b) + ln(c)
    √(b + c) ≠ √b + √c

    cos, ln, and √ are functions - there is no distributive property for functions.
     
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