Question 334113
<pre><b>
{{{30/(1+6e^(-5x))}}}{{{""=""}}}{{{10}}}

Multiply both sides by {{{red((1+6e^(-5x)))}}}

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

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

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

Divide both sides by 10

{{{3}}}{{{""=""}}}{{{1+6e^(-5x)}}}

Subtract 1 from both sides:

{{{2}}}{{{""=""}}}{{{6e^(-5x)}}}

Divide both sides by 6

{{{2/6}}}{{{""=""}}}{{{e^(-5x)}}}

{{{1/3}}}{{{""=""}}}{{{e^(-5x)}}}

Take natural logs of both sides:

{{{ln(1/3)}}}{{{""=""}}}{{{ln(e^(-5x))}}}

Use the identity:  {{{ln(e^A)=A}}}

{{{ln(1/3)}}}{{{""=""}}}{{{-5x}}}

Divide both sides by -5

{{{-ln(1/3)/5}}}{{{""=""}}}{{{x}}}

Get a calculator and do the left sides:

{{{-ln(1/3)/5}}}{{{""=""}}}{{{x}}}

{{{.2197224577}}}{{{""=""}}}{{{x}}}

Edwin</pre>