To evaluate the given expressions using the ALEKS calculator and rounding to the nearest thousandth, let's break down each calculation step-by-step:
### 1. Evaluating [tex]\(\log 23.4\)[/tex]
1. Understand the Expression:
- [tex]\(\log 23.4\)[/tex] means we are looking for the base 10 logarithm of 23.4.
2. Calculate:
- Using a calculator to find the base 10 logarithm of 23.4, enter [tex]\(23.4\)[/tex] and then apply the [tex]\(\log\)[/tex] function.
- According to the precise computations, the result is approximately [tex]\(1.369\)[/tex].
### 2. Evaluating [tex]\(\ln \sqrt{11}\)[/tex]
1. Understand the Expression:
- [tex]\(\ln \sqrt{11}\)[/tex] means we are looking for the natural logarithm (base [tex]\(e\)[/tex]) of the square root of 11.
- Another way to express the square root of 11 is [tex]\(11^{0.5}\)[/tex].
2. Calculate:
- First, compute the square root of 11, which is approximately [tex]\(3.317\)[/tex].
- Next, find the natural logarithm of [tex]\(3.317\)[/tex].
- According to the precise computations, the result is approximately [tex]\(1.199\)[/tex].
### Rounded Results
- For [tex]\(\log 23.4\)[/tex], the answer is [tex]\(1.369\)[/tex].
- For [tex]\(\ln \sqrt{11}\)[/tex], the answer is [tex]\(1.199\)[/tex].
Thus:
[tex]\[
\log 23.4 = 1.369
\][/tex]
[tex]\[
\ln \sqrt{11} = 1.199
\][/tex]
