Question

полагая, что lg3=p, lg2=q, найдите $log_{5}$6.

Answer 1

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)