SOLUTION: I am stuck on this problem. I am supposed to solve for x: e^0.5x=3^(1-2x) Thanks for any assistance you can give.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am stuck on this problem. I am supposed to solve for x: e^0.5x=3^(1-2x) Thanks for any assistance you can give.      Log On


   

Question 534035: I am stuck on this problem. I am supposed to solve for x:
e^0.5x=3^(1-2x)
Thanks for any assistance you can give.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
e%5E0.5x+=+3%5E%281-2x%29 Take the natural log of both sides.
Ln%28e%5E%280.5x%29%29+=+Ln%283%5E%281-2x%29%29 Apply the "power rule" for logarithms.
0.5xLn%28e%29+=+%281-2x%29Ln%283%29 Substitute Ln%28e%29+=+1 and Ln%283%29+=+1.1approx.
0.5x+=+%281-2x%29%281.1%29 Evaluate.
0.5x+=+1.1-2.2x Add 2.2x to both sides.
2.7x+=+1.1 Divide both sides by 2.7
x+=+1.1%2F2.7
x+=+11%2F27
x+=+0.407approx.