Question

expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log y. log x⁴y⁵

Explanation:

Step1: Apply product rule of logs

The product rule of logarithms states that $\log(ab) = \log a + \log b$. So for $\log x^{4}y^{5}$, we can split it as $\log x^{4} + \log y^{5}$.

Step2: Apply power rule of logs

The power rule of logarithms states that $\log a^{n} = n\log a$. Applying this to $\log x^{4}$ gives $4\log x$, and applying it to $\log y^{5}$ gives $5\log y$.

Answer:

$4\log x + 5\log y$