Shouldn't these 2 equations be equal?

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The discussion centers on a misunderstanding of the properties of exponents and logarithms. The original poster mistakenly believed that e^(3ln2) could be expressed as e^3 * e^(ln2), leading to an incorrect conclusion that 2e^3 equals 8. The correct simplification shows that e^(3ln2) equals e^(ln(2^3)), which simplifies to 8. The key takeaway is that e^(x+y) equals e^x * e^y, but e^(xy) does not equal e^x * e^y. This highlights the importance of correctly applying logarithmic and exponential rules in mathematical problems.
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Homework Statement


I was doing a math problem, where I forgot to simplify e3ln2.


Homework Equations





The Attempt at a Solution



Instead of doing e3ln2 = eln(2^3) = eln(8) = 8, I did the following:


e3ln2 = e3*eln2 = 2e3

However, 2e3 ≠ 8.

What happened?
Mod edit: The OP figured it out.
 
Last edited by a moderator:
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Just in case someone stumbles here with the same problem, my mistake was to assume e3ln2 = e3*eln2.

That statement is false since e3*eln2 = e3+ln2 ≠ e3ln2.
 
Well, let's hope that people who are attempting to solve problems like this will know that e^{x+ y}= e^xe^y\ne e^{xy}.
 

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