How to Find the Linear Approximation of $\ln(8-4x)$ at $x = 7/4$, and Use it to Estimate $ln(0.99)$ I am trying to determine how to find the linear approximation of $\ln(8-4x)$ at $x = 7/4$, and use it to estimate $\ln(0.99)$.
So far, I have made the following steps:
1) Find the derivative of $\ln(8-4x)$, which is $-4/(8-4x)$
2) Plug in $x=7/4$ into the derivative to get the slope, which gives $-4$
3) Determine the point-slope expression, which is $y=-4x+7$
4) To estimate $\ln(0.99)$, plug in $0.99$ into the point-slope expression, which gives 3.04.
However, I am not sure that step 4 is correct. Does anyone know how to find the estimate of $ln(0.99)$ in this case?

You found an approximation of $\ln(8 - 4x)$, which you want to use to estimate $\ln(0.99)$. What $x$ gives you $8 - 4x = .99$? It is this $x$ you want to plug into your approximation.
