Question 629620
<pre>
           <font face="symbol">p</font><sup>x+1</sup> = e<sup>5x</sup>

Take natural logs of both sides:

       ln(<font face="symbol">p</font><sup>x+1</sup>) = ln(e<sup>5x</sup>)

Use rules of logarithms:

     (x+1)ln(<font face="symbol">p</font>) = 5x

Distribute to remove parentheses:

x·ln(<font face="symbol">p</font>) + ln(<font face="symbol">p</font>) = 5x

Rearrange equation:

   -5x + x·ln(<font face="symbol">p</font>) = -ln(<font face="symbol">p</font>)

Multiply through both sides by -1:

    5x - x·ln(<font face="symbol">p</font>) = ln(<font face="symbol">p</font>)

Factor out x on the left

      x[5-ln(<font face="symbol">p</font>)] = ln(<font face="symbol">p</font>)

Divide both sides by 5-ln(<font face="symbol">p</font>) 

              x = {{{ln(pi)/(5-ln(pi))}}}

Edwin</pre>