Question

expand the following. \\(\log x^{18}y^3\\) \\(\text{a) } 18\log x - 3\log y\\) \\(\text{b) } 18\log x + \log 3\\) \\(\text{c) } 18\log x + 3\log y\\) \\(\text{d) cannot be expanded}\\)

Explanation:

Step1: Apply product rule of logs

$\log(x^{18}y^3) = \log(x^{18}) + \log(y^3)$

Step2: Apply power rule of logs

$\log(x^{18}) + \log(y^3) = 18\log x + 3\log y$

Answer:

C) $18 \log x + 3 \log y$