Question 253356
<pre><font size = 4 color = "indigo"><b>
We use the change of base formula:

{{{log(a,(x))=log(b,(x))/log(b,(a))}}}

and the basic logarithm formulas.

1.  {{{log(10,(5))=log(3,(5))/log(3,(10))=q/log(3,(5*2))=q/(
log(3,(5))+log(3,(2)) )=q/(q+log(3,(2)))  }}}

therefore  

2.  {{{log(10,(5))=q/(q+log(3,(2)))  }}}



3.  {{{p = log(8,(3))=log(3,(3))/log(3,(8))=1/log(3,(2^3))=1/(3log(3,(2)))}}}

therefore

    {{{p=1/(3log(3,(2))) }}}

    {{{3p*log(3,(2))=1}}}

4.  {{{log(3,(2))=1/(3p)}}}

Substitute equation 4 into equation 2

    {{{log(10,(5))=q/(q+log(3,(2)))  }}}
    {{{log(10,(5))=q/(q +1/(3p))  }}}
    {{{log(10,(5))=(q/(q +1/(3p)))*((3p)/(3p))  }}}
    {{{log(10,(5))=(3pq)/(3pq+1)  }}} 
 
Edwin</pre>