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

1 Answer
Apr 21, 2018

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#