SOLUTION: How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +7

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +7      Log On


   

Question 502985: How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +7
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
How to use exponentials to solve the following equation. (ii)
7+3e(to the power x)=3/e(to the power x+6) +7
:
7 + 3e%5Ex = 3%2Fe%5E%28x%2B6%29 + 7
Subtract 7 from both sides
3e%5Ex = 3%2Fe%5E%28x%2B6%29
Change the sign of the exponent to give us the reciprocal
3%2Fe%5E%28-x%29 = 3%2Fe%5E%28x%2B6%29
when the numerators are equal, the denominators are equal, therefore:
e%5E%28-x%29 = e%5E%28x%2B6%29
therefore
-x = x + 6
-6 = x + x
-6 = 2x
x = -3
:
:
Check this in the original equation
7 + 3e%5E-3 = 3%2Fe%5E%28-3%2B6%29 + 7
Change the sign of the exponent to give us the reciprocal
7 + 3%2Fe%5E%283%29 = 3%2Fe%5E3 + 7