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Evaluate [tex]y = \ln (x - 2)[/tex] for the following values of [tex]x[/tex]. Round to the nearest thousandth.

[tex]x = 3, y \approx[/tex] [tex]\(\square\)[/tex]

[tex]x = 4, y \approx[/tex] [tex]\(\square\)[/tex]

[tex]x = 6, y \approx[/tex] [tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
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].
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