Question

Se log 3 = a, log 5 = b e log 7 = c, quanto vale log 315 em termos de a, b e c?

Answer 1

Temos que $315= 3^2\cdot 5\cdot 7$, então

$log315=log(3^2\cdot 5\cdot 7)$

$log(3^2\cdot 5\cdot 7)=log3^2+log5+log7=2log3+log5+log7=\\2\overbrace{log3}^a+\overbrace{log5}^b+\overbrace{log7}^{c}=2a+b+c\therefore \boxed{log315=2a+b+c}$