SOLUTION: Please help with the following problem Ln square root(x-2) = -2. Thank you

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Question 4877: Please help with the following problem Ln square root(x-2) = -2. Thank you
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Interesting problem. Is this what you mean? ln+%28sqrt+%28x-2%29%29+=+-2

If so, then this is a problem in "inverses", that is, in "undoing" what has been done. Start by undoing the ln, by raising both sides as a power of e. That means
e%5E%28ln+%28sqrt%28x-2%29%29%29+=+e%5E%28-2%29+
sqrt+%28x-2%29+=+e%5E%28-2%29+

Next, undo the sqrt, by squaring both sides of the equation:
%28sqrt+%28x-2%29%29%5E2+=+%28%28e%5E%28-2%29%29%5E2%29+

Remember that when you raise a power to a power, you multiply exponents:
+%28x-2%29+=+e%5E+%28-4%29+

Then to solve for x, add 2 to each side of the equation:
x+=+2+%2B+e%5E%28-4%29+

R^2 at SCC