The Christmas Equation

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   To begin, let’s start with this equation:
Now let’s rearrange a bit by multiplying both sides by r2:
We currently have in this expression a natural logarithm. Since the natural logarithm ln(x) is defined as the inverse function of the exponential function ex, we can remove the logarithm from our equation entirely by raising the number e to the power of our equation:
Now, since ln(ex) is equal to x, we can apply this to our equation to leave only what was in the parentheses on the right side:
To remove the denominator, we have to multiply both sides by m:
Finally, with a little bit more rearranging, we are left with our final expression:

Edited by Hugh Manatee - December 24 2021 at 20:45

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Hugh Manatee Members Profile Send Private Message Find Members Posts Add to Buddy List Reviewer page Forum Senior Member Joined: December 07 2021 Location: The Barricades Status: Offline Points: 1587	Post Options Post Reply Quote Hugh Manatee Report Post Thanks(0) Quote Reply Topic: The Christmas Equation Posted: December 24 2021 at 20:38
	To begin, let’s start with this equation: Now let’s rearrange a bit by multiplying both sides by r2: We currently have in this expression a natural logarithm. Since the natural logarithm ln(x) is defined as the inverse function of the exponential function ex, we can remove the logarithm from our equation entirely by raising the number e to the power of our equation: Now, since ln(ex) is equal to x, we can apply this to our equation to leave only what was in the parentheses on the right side: To remove the denominator, we have to multiply both sides by m: Finally, with a little bit more rearranging, we are left with our final expression: Edited by Hugh Manatee - December 24 2021 at 20:45
	I should have been a pair of ragged claws Scuttling across the floors of uncertain seas

wiz_d_kidd Members Profile Send Private Message Find Members Posts Add to Buddy List Reviewer page Forum Senior Member Joined: January 13 2018 Location: EllicottCityMD Status: Offline Points: 1423	Post Options Post Reply Quote wiz_d_kidd Report Post Thanks(0) Quote Reply Posted: December 25 2021 at 07:20
	Yay! Math for Christmas! Thanks for stimulating my brain cells!