Question

3. Which of the following is equivalent to log
%)
2
(1) log x-logy
1
(3) 3 log x-logy
3
(2) 9log(x - y)
(4) log (3x) - log

Answer 1

Answer:

$\boxed{(3) \: 3 log \: x - \frac{1}{3} log \: y}$

Step-by-step explanation:

$log( \frac{ {x}^{3} }{ \sqrt[3]{y} } ) = log( \frac{ {x}^{3} }{ {y}^{ \frac{1}{3} } } ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = log( {x}^{3} \times {y}^{ - \frac{1}{3} } ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = log \: {x}^{3} + log \: {y}^{ - \frac{1}{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 log \: x + (-\frac{1}{3} log \: y) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 log \: x - \frac{1}{3} log \: y$