Question

Logaritmo
Calcule o valor de Y na expressão:
Y= log 0,001 + log 25 √5

Answer 1

Simplificando as contas:

$Y= \log 0,001 + \log 25 \sqrt{5}\\\\Y=\log 10/10000+\log25+\log\sqrt{5}\\\\Y=\log10-\log10000+\log(100/4)+\log5^{1/2}\\\\Y=\log10-\log10000+\log100-\log4 + 1/2\log5\\\\Y=\log10-\log10000+\log100-\log2^{2} + 1/2\log(10/2)\\\\Y=\log10-\log10000+\log100-2\log2 + 1/2\log10-1/2\log2$

Calculando:

$Y=\log10-\log10000+\log100-2\log2 + 1/2\log10-1/2\log2\\\\Y=1-4+2-(2\cdot 0,3) + 0,5-(1/2\cdot 0,3)\\\\Y=-1-0,6+0,5-0,15\\\\Y=-1,75+0,5\\\\\boxed{Y=-1,25}$

Dúvidas? Comente.