Question

As funções logarítmicas f e g são dadas por f(x) = log3 x e g(x) = log4 x. Determine:
a) f(9)
b) g(1)
c) Im(f)

Answer 1

a) $f(x)=\text{log}_3~x$

$f(9)=\text{log}_3~9$

$3^{f(9)}=9$

$3^{f(9)}=3^2$

$f(9)=2$.

b) $g(x)=\text{log}_4~x$

$g(1)=\text{log}_4~1$

$4^{g(1)}=1$

$4^{g(1)}=4^0$

$g(0)=1$

c) $Im(f)=\mathbb{R}$.