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Homework Help: When are you supposed to take the natural log of both sides of an equation?

  1. Nov 4, 2011 #1
    It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?
    Last edited: Nov 4, 2011
  2. jcsd
  3. Nov 4, 2011 #2
    You use "e" to cancel out a natural log of an equation.
  4. Nov 4, 2011 #3


    Staff: Mentor

    If you have an equation that involves exponents, that's a natural for taking the log of both sides.

    For example, if ex + 2 = 3, we can take the natural log of both sides to get
    ln(ex + 2) = ln(3)
    x + 2 = ln(3)
    x = -2 + ln(3) ≈ -1.307
  5. Nov 4, 2011 #4


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    Homework Helper
    Education Advisor
    Gold Member

    The key to understand is you use an inverse operation or a sequence of inverse operations to reveal a formula for an unknown but sought variable. An exponential function is the inverse of a logarithmic function. You would do something similar if you wanted to clear for an additive inverse or a multiplicative inverse.

    Mark44's example to illustrate is a good one.

    Note that logb(bx)=x
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