expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log…

expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log y. log \\frac{x^{4}}{y^{2}}

expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log y. log \\frac{x^{4}}{y^{2}}

Answer

Explanation:

Step1: Apply quotient rule

The quotient rule of logarithms is $\log\frac{a}{b}=\log a-\log b$. So, $\log\frac{x^{4}}{y^{2}}=\log x^{4}-\log y^{2}$.

Step2: Apply power rule

The power rule of logarithms is $\log a^{n}=n\log a$. For $\log x^{4}$, using the power rule, we get $4\log x$. For $\log y^{2}$, using the power rule, we get $2\log y$.

Answer:

$4\log x - 2\log y$