SOLUTION: ln(1/x) = 2

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Question 35863: ln(1/x) = 2
Found 2 solutions by rapaljer, AnlytcPhil:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
ln+%281%2Fx%29+=+2

First, raise both sides as a power of e, to undo the ln.
e%5E%28ln+%281%2Fx%29%29+=+e%5E2
1%2Fx+=+e%5E2 or 1%2Fx+=+%28e%5E2%29%2F1

There are several ways to do the next step. I like to invert both sides of the equation. In other words, if two quantities are equal, then their reciprocals are also equal. Flip both sides:
x%2F1+=+1%2F%28e%5E2%29 or x+=+e%5E-2

Unfortunately, I left my calculator at the office today, so you'll have to do the calculation yourself.

R^2 at SCC

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
                            ln(1/x) = 2

On the left side, use this rule of logarithms:

  ln(A/B) = ln(A) - ln(B)

with A = 1 and B = x

                      ln(1) - ln(x) = 2

                          0 - ln(x) = 2 

                             -ln(x) = 2

Multiply or divide thru by -1

                              ln(x) = -2

Use this equation-exchange rule:  The equation

 ln(A) = B 

is equivalent to and may be replaced by the equation

    A = eB.

with A = 2 and B = -2 
 
So equation

                             ln(x) = -2 

becomes equation

                                 x = e-2,

or by calculator,                x = .1353352832

Edwin McCravy
AnlytcPhil@aol.com