SOLUTION: I am really stuck on how to answer this question, it says solve the following equation.. {{{ e^(x)=2e^(1-2x) }}} I have already tried making the eqaution equal to 0 and trying t

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am really stuck on how to answer this question, it says solve the following equation.. {{{ e^(x)=2e^(1-2x) }}} I have already tried making the eqaution equal to 0 and trying t      Log On


   



Question 654518: I am really stuck on how to answer this question, it says solve the following equation.. +e%5E%28x%29=2e%5E%281-2x%29+
I have already tried making the eqaution equal to 0 and trying to solve it, but i don't know how to, i also tried logging both sides but im not sure how to as both sides contain x and both have powers.
Thankyou

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
+e%5Ex = 2%2Ae%5E%281-2x%29+
Divide both sides by e%5E%281-2x%29

+e%5Ex%2Fe%5E%281-2x%29 = 2%2Ae%5E%281-2x%29%2Fe%5E%281-2x%29+

Subtract exponents of e on the left, cancel on the right:

+e%5E%28x-%281-2x%29%29 = 2%2Across%28e%5E%281-2x%29%29%2Fcross%28e%5E%281-2x%29%29+

+e%5E%28x-1%2B2x%29 = 2

+e%5E%283x-1%29 = 2

Use the principle that equation e%5EA+=+B is equivalent to the
equation A = ln(B) to rewrite the above as

3x - 1 = ln(2)

    3x = 1 + ln(2)

     x = %281%2Bln%282%29%29%2F3

     x ≈ 0.5643823935

Edwin