Полагая, что lg3=p, lg2=q, найдите [latex] log_{5} [/latex]6.

log(5)6= log(5)2 + log(5)3 = 1/log(2)5 +1/log(3)5=1/log(2)(10/2)+1/log(3)(10/2)= 1/(log(2)10 - log(2)2) + 1/(log(3)10 - log(3)2)= 1/(1/lg2 -1) + 1/(1/lg3 -lg2/lg3) = lg2/(1-lg2) + lg3/(1-lg2)= (lg2 +lg3)/(1-lg2) = (p+q)/(1-q)