Question

Sabendo que log⁡ 2 = -3x, log⁡ 3 = 2y + x e log ⁡5 = z - y, quanto vale log⁡ 60 ? *

a) 3x –y + z

b) 6x + y – 2z

c) -2x -3y + 3z

d) -5x + y + z​

Answer 1

Explicação passo-a-passo:

$\sf log~60=log~(2^2\cdot3\cdot5)$

$\sf log~60=log~2^2+log~3+log~5$

$\sf log~60=2\cdot log~2+log~3+log~5$

$\sf log~60=2\cdot(-3x)+2y+x+z-y$

$\sf log~60=-6x+2y+x+z-y$

$\sf log~60=-6x+x+2y-y+z$

$\sf log~60=-5x+y+z$

Letra D