SOLUTION: y=e^10^2x x=?

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Question 5113: y=e^10^2x
x=?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This looks like a problem in inversing--that is "undoing" the operations.
y=e%5E10%5E%282x%29

Start by undoing the e raised to the power, by taking the ln of each side:
+lny+=ln+%28e%5E10%5E%282x%29%29%7D+
ln+y+=+10%5E%282x%29+

Next, undo 10 raised to the power, by taking the log of each side (that is, log base 10):
log+%28%28ln+y%29%29++=+log+%2810%2C+10%5E%282x%29%29+
log+%28%28ln+y%29%29++=+2x+

Last, divide both sides by 2:
%28log+%28%28ln+y%29%29%29%2F2++=+%282x%29%2F2+
x+=+%281%2F2%29+%2Alog+%28%28ln+y%29%29+

Of course there are many other forms of the answer as well as this one.


R^2 at SCC