To evaluate the function [tex]\( y = \ln (x-2) \)[/tex] for given values of [tex]\( x \)[/tex], we follow these steps:
1. Substitute each [tex]\( x \)[/tex] value into the function [tex]\( y = \ln (x-2) \)[/tex].
2. Compute the natural logarithm (ln) of the resulting value.
3. Round the result to the nearest thousandth.
Let's do this for each given value of [tex]\( x \)[/tex]:
1. When [tex]\( x = 3 \)[/tex]:
[tex]\[
y = \ln (3 - 2) = \ln 1 = 0.0
\][/tex]
Therefore, [tex]\( y = 0.0 \)[/tex].
2. When [tex]\( x = 4 \)[/tex]:
[tex]\[
y = \ln (4 - 2) = \ln 2 \approx 0.693
\][/tex]
Therefore, [tex]\( y \approx 0.693 \)[/tex].
3. When [tex]\( x = 6 \)[/tex]:
[tex]\[
y = \ln (6 - 2) = \ln 4 \approx 1.386
\][/tex]
Therefore, [tex]\( y \approx 1.386 \)[/tex].
So, the values are:
For [tex]\( x = 3 \)[/tex], [tex]\( y = 0.0 \)[/tex].
For [tex]\( x = 4 \)[/tex], [tex]\( y \approx 0.693 \)[/tex].
For [tex]\( x = 6 \)[/tex], [tex]\( y \approx 1.386 \)[/tex].
