Question

find the domain and range of each function
f(x)=log3x

D:_________
R:_________
V.A_________
(V.A stand for vertical asymptote)

Answer 1

any type of logarithm works only for positive numbers so
\[ \large 3x>0\Rightarrow x>0/3=0 \]
so the domain is \((0,+\infty)\)

Answer 2

For the domain, you will be able to determine its value by considering that your base is positive.

Answer 3

the logarithm of a number can be positive or negative so the range is \(\mathbb{R}\)

Answer 4

a logarithmic function has a vertical asymptote when its argument is zero. so
\[ \large 3x=0\Rightarrow x=0/3=0 \]
therefore VA: x=0