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Simplifying logaritm

  • Thread starter Rectifier
  • Start date
  • #1
Rectifier
Gold Member
313
4
Hey there!
I am getting two completely different equations when I try to simplify one.
What am I doing wrong?

1.
[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]

2.
[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 :)
 

Answers and Replies

  • #2
33,075
4,776
Hey there!
I am getting two completely different equations when I try to simplify one.
What am I doing wrong?

1.
[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]
It should be ##e^{ln(2) + ln(x)} = e^{ln(2)} \cdot e^{ln(x)} ## in your third step.
2.
[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 :)
 
  • #3
Rectifier
Gold Member
313
4
Oh! Thank you Mark!
 

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