Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. \[ \log _{4}\left(\frac{4 \sqrt{9}}{7}\right) \] A. $\left(\log _{4} 4\right)\left(\frac{1}{2} \log _{4} 9\right)-\log _{4} 7$ B. $\log _{4} 4+\sqrt{\log _{4} 9}-\log _{4} 7$ C. $\frac{\log _{4} 4+\frac{1}{2} \log _{4} 9}{\log _{4} 7}$ D. $\log _{4} 4+\frac{1}{2} \log _{4} 9-\log _{4} 7$

Step 1 ：Rewrite the given expression using the properties of logarithms: \(\log _{4}\left(\frac{4 \sqrt{9}}{7}\right) = \log _{4} 4 + \log _{4} \sqrt{9} - \log _{4} 7\)

Step 2 ：Simplify the expression by recognizing that the square root of a number is the same as raising that number to the power of 1/2: \(\log _{4} 4 + \log _{4} 9^{1/2} - \log _{4} 7 = \log _{4} 4 + \frac{1}{2} \log _{4} 9 - \log _{4} 7\)

Step 3 ：Further simplify the expression by recognizing that the logarithm of a number to the same base is 1: \(1 + \frac{1}{2} \log _{4} 9 - \log _{4} 7\)

Step 4 ：Final Answer: \(\boxed{\log _{4} 4+\frac{1}{2} \log _{4} 9-\log _{4} 7}\)