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Simplifying logaritm

  1. Apr 25, 2014 #1


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    Gold Member

    Hey there!
    I am getting two completely different equations when I try to simplify one.
    What am I doing wrong?

    [tex]y=ln(2x) \ \Leftrightarrow \ y=ln(2) + ln(x) \ \Leftrightarrow \ e^y=e^{ln(2)}+e^{ln(x)} \ \Leftrightarrow \ e^y=2+x [/tex]

    [tex]y=ln(2x) \ \Leftrightarrow \ e^y=e^{ln(2x)} \ \Leftrightarrow \ e^y=2x [/tex]

    I am sorry if its something completely obvious. Its pretty late here so my brain doesn't function properly :)
  2. jcsd
  3. Apr 25, 2014 #2


    Staff: Mentor

    It should be ##e^{ln(2) + ln(x)} = e^{ln(2)} \cdot e^{ln(x)} ## in your third step.
  4. Apr 25, 2014 #3


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    Gold Member

    Oh! Thank you Mark!
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