Question

How do you find the domain, x intercept and vertical asymptotes of `y=log_10(x/5)`?

Answer 1

See details below

Explanation:

`Log_bx` is a continous function and to define a real number the argument x need to be positive. Then in our case

`x/5>0`. That means `x>0`

Domain is `Dom (y)=(0,+oo)`

x intercept : We know that `log_bx=0` only when `x=1`. Then in our case `x/5=1`. This occur only if `x=5`

Vertical asymptotes : We also know that `lim_(xto0)Log_bx=-oo`. Then in our case it is the same trend, so vertical asymptote is `x=0`