Question

Which of the following is equivalent to log(x³/³√y)?

a) log x - log y
b) 9 log(x - y)
c) 3 log x - 1/3 log y
d) log(3x) - log(y/3)

Answer 1

The expression log(x³/³√y) is equivalent to 3 * log(x) - (1/3) * log(y).

Step-by-step explanation:

The given expression is log(x³/³√y). To simplify this expression, we can use the property of logarithms that states that log(a/b) = log(a) - log(b).

In this case, we can rewrite the expression as log(x³) - log(³√y). Now, we can apply the rule that log(a^b) = b * log(a) to the first term, giving us 3 * log(x) - log(³√y). Finally, we can simplify the expression further by using the rule that log(³√y) = (1/3) * log(y). Therefore, the expression is equivalent to 3 * log(x) - (1/3) * log(y).