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

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

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Question 334113: 30%2F%281%2B6e%5E%28-5x%29%29%27%27=%27%2710
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(30993) 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(8893) About Me  (Show Source):
You can put this solution on YOUR website!

30%2F%281%2B6e%5E%28-5x%29%29%27%27=%27%2710

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%27%27=%27%2710red%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%27%27=%27%2710red%28%281%2B6e%5E%28-5x%29%29%29

30%27%27=%27%2710%281%2B6e%5E%28-5x%29%29

Divide both sides by 10

3%27%27=%27%271%2B6e%5E%28-5x%29

Subtract 1 from both sides:

2%27%27=%27%276e%5E%28-5x%29

Divide both sides by 6

2%2F6%27%27=%27%27e%5E%28-5x%29

1%2F3%27%27=%27%27e%5E%28-5x%29

Take natural logs of both sides:

ln%281%2F3%29%27%27=%27%27ln%28e%5E%28-5x%29%29

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

ln%281%2F3%29%27%27=%27%27-5x

Divide both sides by -5

-ln%281%2F3%29%2F5%27%27=%27%27x

Get a calculator and do the left sides:

-ln%281%2F3%29%2F5%27%27=%27%27x

.2197224577%27%27=%27%27x

Edwin