What is the x-intercept of f(x) = log4x?

Question

This is my final question on my homework page, and I am having a complete brain fart. Help would be greatly appreciated as to how I find the x-intercept. Thank you!

Answer 1

By definition of a logarithm

log_ax = n then aⁿ = x

 

log(4x) = 0

10⁰ = 4x

1 = 4x

x = 1/4

x intercept at (1/4, 0)

Answer 2

The x-intercept is where f(x) = 0

 

log(4x) = 0

 

log4 + logx = 0

 

logx = -log4

 

x = 10^-log4

 

The x-intercept is the point (10^-log4, 0)

 

Test the solution:

 

Is f(10^-log4) = 0 ?

 

f(10^-log4) = log[4(10^-log4)] = log4 + log(10^-log4) = log4 - log4 = 0