Question 1177521
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Given:
{{{log(8,3)=P}}}
{{{log(3,5)=Q}}}<br>
Given those bases and arguments, it is almost certain that we will be working the problem using base 3 logarithms.  So
{{{log(3,8) = 1/P}}}<br>
Then<br>
{{{log(10,5) = log(3,5)/log(3,10) = log(3,5)/(log(3,5)+log(3,2)) = Q/(Q+log(3,2))}}}<br>
{{{log(3,8) = 1/P}}}
{{{log(3,2^3) = 1/P}}}
{{{3*log(3,2) = 1/P}}}
{{{log(3,2) = 1/(3P)}}}<br>
And finally<br>
{{{log(10,5) = Q/(Q+1/(3P))}}}<br>
Simplify/change format if required....<br>