Question

evaluate $y = \ln{(x - 2)}$ for the following values of $x$. round to the nearest thousandth.
$x = 3, y = \square$
$x = 4, y \approx \square$
$x = 6, y \approx \square$

Explanation:

Step1: Substitute x=3 into the function

Substitute $x=3$ into $y=\ln(x-2)$:
$y=\ln(3-2)=\ln(1)$

Step2: Calculate the natural log value

$\ln(1)=0$

Step3: Substitute x=4 into the function

Substitute $x=4$ into $y=\ln(x-2)$:
$y=\ln(4-2)=\ln(2)$

Step4: Calculate and round $\ln(2)$

$\ln(2)\approx0.693$

Step5: Substitute x=6 into the function

Substitute $x=6$ into $y=\ln(x-2)$:
$y=\ln(6-2)=\ln(4)$

Step6: Calculate and round $\ln(4)$

$\ln(4)\approx1.386$

Answer:

$x=3, y=0$
$x=4, y=0.693$
$x=6, y=1.386$