SOLUTION: Solve x in terms of y. Question: y = (e^x + e^-x)/(e^x - e^-x) Answer: x= 1/2 ln ((y+1)/(y-1)) I have the answer with me, but I don’t know how to solve the question ste

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve x in terms of y. Question: y = (e^x + e^-x)/(e^x - e^-x) Answer: x= 1/2 ln ((y+1)/(y-1)) I have the answer with me, but I don’t know how to solve the question ste      Log On


   

Question 1122979: Solve x in terms of y.
Question:
y = (e^x + e^-x)/(e^x - e^-x)
Answer:
x= 1/2 ln ((y+1)/(y-1))
I have the answer with me, but I don’t know how to solve the question step by step.
Thank you so much for the help.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+%28e%5Ex+%2B+e%5E%28-x%29%29%2F%28e%5Ex+-+e%5E%28-x%29%29

Multiply right side by e%5Ex%2Fe%5Ex

y+=+expr%28e%5Ex%2Fe%5Ex%29%28%28e%5Ex+%2B+e%5E%28-x%29%29%2F%28e%5Ex+-+e%5E%28-x%29%29%29

Simplify:

y+=+%28e%5E%282x%29+%2B+e%5E0%29%2F%28e%5E%282x%29+-+e%5E0%29

Simplify:

y+=+%28e%5E%282x%29+%2B+1%29%2F%28e%5E%282x%29+-+1%29

Multiply both sides by e%5E%282x%29-1

y%28e%5E%282x%29+-+1%29+=+e%5E%282x%29+%2B+1

Distribute on left:

y%2Ae%5E%282x%29+-+y+=+e%5E%282x%29+%2B+1

Get terms in e%5E%282x%29 on left side, others on right:

y%2Ae%5E%282x%29+-++e%5E%282x%29+=+y+%2B+1

Factor out e%5E%282x%29 on the left side:

e%5E%282x%29%28y-1%29+=+y+%2B+1

Divide both sides by y-1

e%5E%282x%29+=+%28y+%2B+1%29%2F%28y-1%29
 
Take natural logs of both sides:

ln%28e%5E%282x%29%29+=+ln%28%28y+%2B+1%29%2F%28y-1%29%29

2x%2Aln%28e%29+=+ln%28%28y+%2B+1%29%2F%28y-1%29%29

2x%281%29+=+ln%28%28y+%2B+1%29%2F%28y-1%29%29

2x+=+ln%28%28y+%2B+1%29%2F%28y-1%29%29

Multiply both sides by 1%2F2

expr%281%2F2%292x+=+expr%281%2F2%29ln%28%28y+%2B+1%29%2F%28y-1%29%29

x+=+expr%281%2F2%29ln%28%28y+%2B+1%29%2F%28y-1%29%29

Edwin