Question

Expand the logarithm fully using the properties of logs. Express the final answer interms of log a, and log y.

Answer 1

To solve this problem, we will use these rules

$\begin{gathered} \log ab=\log a+\log b\rightarrow(1) \\ \log a^n=n\log a\rightarrow(2) \end{gathered}$

The given expression is

$\log x^5y$

By using rule (1)

$\log x^5y=\log x^5+\log y$

Use the rule (2) with log x^5

$\log x^5=5\log x$

Then the last answer is

$\log x^5y=5\log x+\log y$

The answer is 5 log x + log y