SOLUTION: {{{30/(1+6e^(-5x))}}}{{{""=""}}}{{{10}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{30/(1+6e^(-5x))}}}{{{""=""}}}{{{10}}}      Log On


   

Question 334113: 30%2F%281%2B6e%5E%28-5x%29%29%22%22=%22%2210
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
30%2F%281%2B6e%5E%28-5x%29%29=10
%281%2B6e%5E%28-5x%29%29=3
6e%5E%28-5x%29=2
e%5E%28-5x%29=1%2F3
-5x = ln(1/3)
x = -ln(1/3)/5
x =~ 0.219722

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

30%2F%281%2B6e%5E%28-5x%29%29%22%22=%22%2210

Multiply both sides by red%28%281%2B6e%5E%28-5x%29%29%29

30%2F%281%2B6e%5E%28-5x%29%29red%28%281%2B6e%5E%28-5x%29%29%29%22%22=%22%2210red%28%281%2B6e%5E%28-5x%29%29%29

30%2F%28cross%281%2B6e%5E%28-5x%29%29%29red%28%28cross%281%2B6e%5E%28-5x%29%29%29%29%22%22=%22%2210red%28%281%2B6e%5E%28-5x%29%29%29

30%22%22=%22%2210%281%2B6e%5E%28-5x%29%29

Divide both sides by 10

3%22%22=%22%221%2B6e%5E%28-5x%29

Subtract 1 from both sides:

2%22%22=%22%226e%5E%28-5x%29

Divide both sides by 6

2%2F6%22%22=%22%22e%5E%28-5x%29

1%2F3%22%22=%22%22e%5E%28-5x%29

Take natural logs of both sides:

ln%281%2F3%29%22%22=%22%22ln%28e%5E%28-5x%29%29

Use the identity:  ln%28e%5EA%29=A

ln%281%2F3%29%22%22=%22%22-5x

Divide both sides by -5

-ln%281%2F3%29%2F5%22%22=%22%22x

Get a calculator and do the left sides:

-ln%281%2F3%29%2F5%22%22=%22%22x

.2197224577%22%22=%22%22x

Edwin