Question

( UF-SE) se log (5x) - 4 . log 5 = -3, então x é igual a:

a) 0,025
b) 0,125
c) 0,25
d) 1,25
e) 2,5

Answer 1

$log \ (5x)-4 \cdot log \ 5 = -3\\ \\log \ (5x)-log \ 5^4 = -3\\ \\log \ (5x)-log \ 625 = -3\\ \\log \ ( \frac{5x}{625}) = -3\\ \\ \frac{5x}{625}=10^{-3}\\ \\ \frac{5x}{625}=\frac{1}{1000}\\ \\ x=\frac{625\cdot1}{5\cdot1000}\\ \\ x=\frac{625}{5000}\\ \\ x=\frac{125}{1000}\\ \\x=0,125$

Answer 2

Olá Lorena

log(5x) - 4*log(5) = -3 

log(x) + log(5) - 4*log(5) = -3

log(x) = 3*log(5) - log(1000)

log(x) = log(125) - log(1000)

log(x) = log(125/1000)

x = 1/8 = 0.125 (B) 

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