Question

Considere a função f(x) = log5 x.
O valor de f (100) – f (4) é:

a) 2
b) 25
c) 20
d) 10
e) 5

Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf log_{c}~a-log_{c}~b=log_{c}~\dfrac{a}{b}$

• $\sf log_{a}~a=1$

Temos:

• $\sf f(100)$

$\sf f(x)=log_{5}~x$

$\sf f(100)=log_{5}~100$

• $\sf f(4)$

$\sf f(x)=log_{5}~x$

$\sf f(4)=log_{5}~4$

Assim:

$\sf f(100)-f(4)=log_{5}~100-log_{5}~4$

$\sf f(100)-f(4)=log_{5}~\dfrac{100}{4}$

$\sf f(100)-f(4)=log_{5}~25$

$\sf f(100)-f(4)=log_{5}~5^2$

$\sf f(100)-f(4)=2\cdot log_{5}~5$

$\sf f(100)-f(4)=2\cdot1$

$\sf f(100)-f(4)=2$

Letra A