Question

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

Explanation:

Step1: Substitute \( x = 3 \) into \( y=\ln(x - 2) \)

Substitute \( x = 3 \) into the function: \( y=\ln(3 - 2)=\ln(1) \). Since \( \ln(1)=0 \), so when \( x = 3 \), \( y = 0 \).

Step2: Substitute \( x = 4 \) into \( y=\ln(x - 2) \)

Substitute \( x = 4 \) into the function: \( y=\ln(4 - 2)=\ln(2) \). Calculate \( \ln(2)\approx0.6931 \) (rounded to the nearest thousandth).

Step3: Substitute \( x = 6 \) into \( y=\ln(x - 2) \)

Substitute \( x = 6 \) into the function: \( y=\ln(6 - 2)=\ln(4) \). Since \( \ln(4) = 2\ln(2)\approx2\times0.6931 = 1.3863 \) (rounded to the nearest thousandth).

Answer:

When \( x = 3 \), \( y = 0 \); when \( x = 4 \), \( y\approx0.693 \); when \( x = 6 \), \( y\approx1.386 \)