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Math Help - simplification of a logarithm

  1. #1
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    simplification of a logarithm

    Original problem is 2e^{3x+5}=6. Ive gotten it to ln e^{3x+5}=ln3. Ordinarily I would change the 3x+5 into the coefficient of lne and go from there but in the example problem Im looking at they simply remove the ln e. Basically this is what they did: They took ln e^{3x+5}=ln3 and simplified it to 3x+5=ln 3. So my question is what rule or property did they use to get rid of the LN e?
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  2. #2
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    They combined two rules. First, they converted the exponent to a coefficient, like you were going to do. Then, they used the rule \ln{e} = 1. Multiplication by 1 doesn't change anything so you are left with just the coefficient.
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  3. #3
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    Quote Originally Posted by mgrade2000 View Post
    Original problem is 2e^{3x+5}=6. Ive gotten it to ln e^{3x+5}=ln3. Ordinarily I would change the 3x+5 into the coefficient of lne and go from there but in the example problem Im looking at they simply remove the ln e. Basically this is what they did: They took ln e^{3x+5}=ln3 and simplified it to 3x+5=ln 3. So my question is what rule or property did they use to get rid of the LN e?
    Yep, ln of e is 1.
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  4. #4
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    ln(e)=1 as does e^ln
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