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How to solve for:

-e3.4e^(2-2n)-9=-4

 Nov 23, 2015
 #1
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-e3.4e^(2-2n)-9=-4  THIS EQUATION HAS ONLY COMPLEX SOLUTION:

 

Solve for n:
-9-9.24216 e^(2-2 n) = -4

-9-9.24216 e^(2-2 n) = -9-9.24216 e^(2-2 n):
-9-9.24216 e^(2-2 n) = -4

Add 9 to both sides:
-9.24216 e^(2-2 n) = 5

Divide both sides by -9.24216:
e^(2-2 n) = -0.540999

Take reciporicals of both sides:
e^(2 n-2) = -1.84843

Take the natural logarithm of both sides:
2 n-2 = 0.614338+i pi (2 k+1)  for  k element Z

Add 2 to both sides:
2 n = 2.61434+i pi (2 k+1)  for  k element Z

Divide both sides by 2:
Answer: |  n = 1.30717+1/2 i pi (2 k+1)  for  k element Z
 

 Nov 24, 2015

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