Logarithmic calculation Let log83 = P, log35 = q, then lg5 =?

Logarithmic calculation Let log83 = P, log35 = q, then lg5 =?

Using the formula of changing bottom
p=lg3/lg8=lg3/3lg2
lg2=lg3/(3p)
q=lg5/lg3
lg3=lg5/q
Substituting LG2 = Lg3 / (3P)
lg2=lg5/(3pq)
lg2=1-lg5
So 1-lg5 = lg5 / (3pq)
lg5=1/[1+1/(3pq)]=3pq/(3pq+1)