Question

write the following logarithmic expression as a single logarithm.

\\2 \log_{4}(x) + 4 \log_{4}(y) = \\

Explanation:

Step1: Apply the power property of logarithms

$$2\log_{4}(x) + 4\log_{4}(y) = \log_{4}(x^{2}) + \log_{4}(y^{4})$$

Step2: Apply the product property of logarithms

$$\log_{4}(x^{2}) + \log_{4}(y^{4}) = \log_{4}(x^{2}y^{4})$$

Answer:

\(\log_{4}(x^{2}y^{4})\)