question 1-9\nwhat is the value of \\(\\log_{2} \\sqrt{32}\\)?\n\\(\\circ\\) 16\n\\(\\circ\\)…

Explanation:

Step1: Rewrite the radical as an exponent

We know that $\sqrt{32} = 32^{\frac{1}{2}}$. Also, $32 = 2^5$, so we can rewrite $32^{\frac{1}{2}}$ as $(2^5)^{\frac{1}{2}}$. Using the exponent rule $(a^m)^n=a^{mn}$, we get $(2^5)^{\frac{1}{2}} = 2^{\frac{5}{2}}$. So the expression becomes $\log_{2}2^{\frac{5}{2}}$.

Step2: Apply the logarithm power rule

The logarithm power rule states that $\log_{a}a^b = b$ (since $\log_{a}x=y$ means $a^y = x$, and if $x = a^b$, then $y = b$). For $\log_{2}2^{\frac{5}{2}}$, here $a = 2$ and $b=\frac{5}{2}$, so by the power rule, $\log_{2}2^{\frac{5}{2}}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$ (corresponding to the option with $\frac{5}{2}$)