Question

Sendo log a = 11, log b = 0,5 , log c = 6 e log(ab²/∛c) = x, o valor de x é:

A) 5
B) 10
C) 15
D) 20
E) 25

Answer 1

log (ab² / ∛c) = log (ab²) - log ∛c

= log a + log b² - log (c^1/3)
= log a + 2log b - (1/3 * log c)
= log a + 2log b - (log c)/3
= 11 + 2(0,5) - 6/3
= 11 + 1 - 2
= 12 - 2
= 10
Letra b.

Answer 2

$log ( \frac{ab^{2}}{ \sqrt[3]{c}} )=x \\ \\ logab^{2}-log \sqrt[3]{c} =x \\ \\ log a + 2.logb-log c^{ \frac{1}{3} }=x \\ \\ log a + 2.logb- \frac{1}{3} log c = x \\ \\ 11+2.0,5- \frac{1}{3} .6=x \\ \\ 11+1-2=x \\ \\ x = 10$

Alternativa B)

Espero ter ajudado.