9) which of the following is equal to \\(\\log \\sqrt4{1,000}\\)? (5 points) \\(\\frac{4}{3}\\)…
9) which of the following is equal to \\(\\log \\sqrt4{1,000}\\)? (5 points) \\(\\frac{4}{3}\\) \\(-\\frac{3}{4}\\) \\(\\frac{3}{4}\\) \\(-\\frac{4}{3}\\)
Answer
Explanation:
Step1: Rewrite root as exponent
$\log \sqrt[4]{1000} = \log (1000)^{\frac{1}{4}}$
Step2: Apply log power rule
$\log (1000)^{\frac{1}{4}} = \frac{1}{4}\log 1000$
Step3: Rewrite 1000 as power of 10
$\frac{1}{4}\log 10^3$
Step4: Simplify log term
$\frac{1}{4} \times 3 = \frac{3}{4}$
Answer:
$\frac{3}{4}$ (Option: $\frac{3}{4}$)