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

`\boxed{(3) \: 3 log \: x - (1)/(3) log \: y}`

Explanation:

`log( \frac{ {x}^(3) }{ \sqrt[3]{y} } ) = log( \frac{ {x}^(3) }{ {y}^{ (1)/(3) } } ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = log( {x}^(3) * {y}^{ - (1)/(3) } ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = log \: {x}^(3) + log \: {y}^{ - (1)/(3) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 log \: x + (-(1)/(3) log \: y) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 log \: x - (1)/(3) log \: y`