Question

How do you find the x intercept of `q(x) = ln ( x - 7 ) + 4`?

Answer 1

`x= e^-4+7 ~= 7.0183`

Explanation:

`q(x) = ln(x-7)+4`

The x intercept of `q(x)` occurs where `q(x) = 0`

I.e. where: `ln(x-7)+4 = 0`

`ln(x-7) = -4`

Remember that `ln e =1`

`:. ln (x-7) = -4lne`

`ln (x-7) = ln e^-4`

Since: `ln a = ln b -> a=b`

`x-7 = e^-4`

`x= e^-4 +7 ~= 7.0183`

The x intercept can be seen on the graph of `g(x)` below:

graph{ln(x-7) +4 [-1.625, 18.375, -2.6, 7.4]}