Expert: Sherman D. - 1/22/2006

Question
Can you please help me with this question.

Find the domain, vertical asymptote, and the x-intercept of f(x)= log4 (5-x).


Answer
f(x) = log(4)(5 - x)
f(x) = (log(5 - x))/(log(4))

in log(x), "x" can't be 0 and anything above 5 will give you a negative value and "x" can't be negative.

Domain : x < 5

since the problem can't go past 5

VA = x = 5

x-intercept is whenever f(x) is 0

0 = (log(5 - x))/(log(4))
log(5 - x) = 0
5 - x = 1
-x = -4
x = 4

Domain : x < 5
VA = 5
x-intercept = 4

For a graph, go to www.calculator.com/calcs/GCalc.html and type in (log(5 - x))/(log(4)) and click enter on the keyboard and you will get a graph.