24. what is the fully expanded form of $log(x^{3}y^{5})$?\n$\bigcirc$ $log x^{5} + log y^{3}$\n$\bigcirc$…

24. what is the fully expanded form of $log(x^{3}y^{5})$?\n$\bigcirc$ $log x^{5} + log y^{3}$\n$\bigcirc$ $5log x + 3log 7$\n$\bigcirc$ $3log x + 5log y$\n$\bigcirc$ $log x^{3} + log y^{5}$

24. what is the fully expanded form of $log(x^{3}y^{5})$?\n$\bigcirc$ $log x^{5} + log y^{3}$\n$\bigcirc$ $5log x + 3log 7$\n$\bigcirc$ $3log x + 5log y$\n$\bigcirc$ $log x^{3} + log y^{5}$

Answer

Explanation:

Step1: Apply product log rule

$\log(x^3 y^5) = \log(x^3) + \log(y^5)$

Step2: Apply power log rule

$\log(x^3) = 3\log x$, $\log(y^5) = 5\log y$

Step3: Combine the results

$3\log x + 5\log y$

Answer:

$\boldsymbol{3\log x + 5\log y}$ (corresponding to the third option)