Someone explain this to me.
Someone explain this to me
Austin Cooper
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Henry Cruz
thats just how exponential functions work famalam, e shows up everywhere
Justin Nguyen
nice non-explanation
Nolan Butler
take the log base x of both sides, then apply the change of base formula to rewrite your equation in terms of natural logarithms and see what you get.
Andrew Rogers
bump
Ian Reyes
I wish I could find an equation to that weird curve there but unfortunately I can't.
Anyways, there is a simple explanation.
Instead of working with two functions lets deal with constants. Set x=2 and get
2^y = y^2
There is the trivial solution y=2 but notice that y=4 also works. Do the same analysis now with e.
e^x = x^e
The only solution there is x=e so there is no magical second solution which, if you notice, is what defines that second curve.
Robert Morales
>The only solution there is x=e so there is no magical second solution
But whyyyyyy
John Gonzalez
>I wish I could find an equation to that weird curve there but unfortunately I can't.
Do you mean Lambert function?
Adrian Watson
But why isn't there. It's been proven that (2,4) and (4,2) are the only whole number solutions if x != y. But why is it that every single positive number has two other positive numbers that when raised to eachother's power will equal the first number. Why is e the exception?
John Evans
x^y = y^x is the same as e ^ y ln(x) = e ^ x ln(y)