Question

Using the Quotient Rule of Logarithms, the Product Rule of Logarithms, and the Power Rule of Logarithms, how can log(x^2/5y) be fully expanded?(1 point) Responses logx−log5−logy logarithm x minus logarithm 5 minus logarithm y logx2−log(5y) logarithm x squared minus logarithm left parenthesis 5 y right parenthesis 2logx−log(5y) 2 logarithm x minus logarithm left parenthesis 5 y right parenthesis 2logx−log5−logy

Answer 1

The expansion of log(x^2/5y) can be done using the Quotient Rule of Logarithms, which states that log(a/b) is equal to log(a) - log(b).

Therefore, log(x^2/5y) can be written as log(x^2) - log(5y).

Using the Power Rule of Logarithms, which states that log(a^b) is equal to b*log(a), we can further simplify it as 2log(x) - log(5y).

So, the fully expanded form of log(x^2/5y) is 2log(x) - log(5y).