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: Evaluate for \( x = 3 \)

Substitute \( x = 3 \) into \( y=\ln(x - 2) \). So we have \( y=\ln(3 - 2)=\ln(1) \). Since \( \ln(1)=0 \), then \( y = 0 \).

Step2: Evaluate for \( x = 4 \)

Substitute \( x = 4 \) into \( y=\ln(x - 2) \). We get \( y=\ln(4 - 2)=\ln(2) \). Using a calculator, \( \ln(2)\approx0.693 \) (rounded to the nearest thousandth).

Step3: Evaluate for \( x = 6 \)

Substitute \( x = 6 \) into \( y=\ln(x - 2) \). This gives \( y=\ln(6 - 2)=\ln(4) \). Since \( \ln(4)=2\ln(2)\approx2\times0.693 = 1.386 \) (rounded to the nearest thousandth).

Answer:

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