Answer: To expand the expression log6(x^3/7y), we can use the logarithmic properties, specifically the power rule and quotient rule of logarithms.
The power rule states that log(base b) (x^a) can be expanded as a * log(base b) (x), and the quotient rule states that log(base b) (x/y) can be expanded as log(base b) (x) - log(base b) (y).
Applying these rules, let's expand the given expression step by step:
log6(x^3/7y)
Using the power rule: 3 * log6(x/7y)
Applying the quotient rule: 3 * (log6(x) - log6(7y))
Simplifying: 3 * (log6(x) - (log6(7) + log6(y)))
Further simplifying: 3 * (log6(x) - log6(7) - log6(y))
Therefore, the expanded form of the expression log6(x^3/7y) is 3 * (log6(x) - log6(7) - log6(y)).