16) condense (rewrite as a single logarithm) and simplify if possible. $5\\log_{4}(x) + 3\\log_{4}(y)…

16) condense (rewrite as a single logarithm) and simplify if possible. $5\\log_{4}(x) + 3\\log_{4}(y) - \\log_{4}(xy)$ (5 points) $\\circ \\log_{4}\\left(x^{5}y^{3}-xy\\right)$ $\\circ \\log_{4}(15)$ $\\circ \\log_{4}(14xy)$ $\\circ \\log_{4}\\left(x^{4}y^{2}\\right)$

16) condense (rewrite as a single logarithm) and simplify if possible. $5\\log_{4}(x) + 3\\log_{4}(y) - \\log_{4}(xy)$ (5 points) $\\circ \\log_{4}\\left(x^{5}y^{3}-xy\\right)$ $\\circ \\log_{4}(15)$ $\\circ \\log_{4}(14xy)$ $\\circ \\log_{4}\\left(x^{4}y^{2}\\right)$

Answer

Explanation:

Step1: Apply power rule to logs

$5\log_4(x) = \log_4(x^5)$, $3\log_4(y) = \log_4(y^3)$ Expression becomes: $\log_4(x^5) + \log_4(y^3) - \log_4(xy)$

Step2: Apply product rule to sum

$\log_4(x^5) + \log_4(y^3) = \log_4(x^5y^3)$ Expression becomes: $\log_4(x^5y^3) - \log_4(xy)$

Step3: Apply quotient rule to difference

$\log_4(x^5y^3) - \log_4(xy) = \log_4\left(\frac{x^5y^3}{xy}\right)$

Step4: Simplify the argument

$\frac{x^5y^3}{xy} = x^{5-1}y^{3-1} = x^4y^2$ Expression becomes: $\log_4(x^4y^2)$

Answer:

$\log_4(x^4y^2)$ (corresponding to the last option)