Полагая, что lg3=p, lg2=q, найдите 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)