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

Feb 28, 2017

$x = {e}^{-} 4 + 7 \cong 7.0183$

#### Explanation:

$q \left(x\right) = \ln \left(x - 7\right) + 4$

The x intercept of $q \left(x\right)$ occurs where $q \left(x\right) = 0$

I.e. where: $\ln \left(x - 7\right) + 4 = 0$

$\ln \left(x - 7\right) = - 4$

Remember that $\ln e = 1$

$\therefore \ln \left(x - 7\right) = - 4 \ln e$

$\ln \left(x - 7\right) = \ln {e}^{-} 4$

Since: $\ln a = \ln b \to a = b$

$x - 7 = {e}^{-} 4$

$x = {e}^{-} 4 + 7 \cong 7.0183$

The x intercept can be seen on the graph of $g \left(x\right)$ below:

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