Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations. \[ \begin{array}{r} \log \frac{32}{5}=[1] \\ \log \sqrt{5}=\square \end{array} \]
Solution
Step 1 ：The problem is asking for the logarithm of two different expressions. The base of the logarithm is not specified, so we will assume it is base 10 (common logarithm).
Step 2 ：The first expression is the logarithm of 32/5. We can calculate this directly.
Step 3 ：The second expression is the logarithm of the square root of 5. We can simplify this expression by recognizing that the square root of a number is the same as raising that number to the 1/2 power. Therefore, we can rewrite the expression as \(\log(5^{1/2})\).
Step 4 ：Calculate \(\log\left(\frac{32}{5}\right)\) to get approximately 0.8061799739838872.
Step 5 ：Calculate \(\log\left(\sqrt{5}\right)\) to get approximately 0.34948500216800943.
Step 6 ：Round the results to the nearest thousandth to get the final answers: \(\log\left(\frac{32}{5}\right) = \boxed{0.806}\) and \(\log\left(\sqrt{5}\right) = \boxed{0.349}\).
