Question

How do find the x-intercept of `f(x)=2log4(x)`?

Answer 1

`(1/4, 0)`

Explanation:

The x-intercept occurs where the graph intercepts the x-axis - in other words, where `f(x) = 0`. So, all we have to do is set `f(x)` equal to `0` and solve for `x`. Let's do it:

`0 = 2log4x` (setting `f(x)` equal to 0)
`0 = log4x` (dividing by `2`)
`10^0 = 10^(log4x)` (10 to the power of both sides, to cancel out logarithm)
`1 = 4x` (simplifying; `10^0 = 1`, `10^(log4x) = 4x`)
`x = 1/4` (dividing by `4` to isolate `x`)

Thus, the x-intercept of `f(x) = 2log4x` occurs at the point `(1/4, 0)`.