Problem

$\log _{2} \frac{\sqrt{x}}{a^{2}}$

Answer

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Answer

So, the simplified form of the expression \(\log _{2} \frac{\sqrt{x}}{a^{2}}\) is \(\boxed{-2\log(a) + 0.5\log(x)}\)

Steps

Step 1 ：Given the expression \(\log _{2} \frac{\sqrt{x}}{a^{2}}\)

Step 2 ：We can use the properties of logarithms to simplify this expression.

Step 3 ：Applying the property \(\log_b(m/n) = \log_b(m) - \log_b(n)\), we get \(-\log(a^{2}) + \log(\sqrt{x})\)

Step 4 ：Next, applying the property \(\log_b(m^n) = n \log_b(m)\), we get \(-2\log(a) + 0.5\log(x)\)

Step 5 ：So, the simplified form of the expression \(\log _{2} \frac{\sqrt{x}}{a^{2}}\) is \(\boxed{-2\log(a) + 0.5\log(x)}\)

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