You can put this solution on YOUR website! see my worksheet below.
the answer is log(y^(25/3)/x^2).
this answer has been verified to be correct by assigning 5 to x and 6 to y and evaluating both the original expression and the final expression to determine if they yielded the same answer.
they did.
i rewrote your original expression to the following, based on my understanding of what you had written.
log(x^4 * y^5) - 2 * log(x * y^(1/3)) - 4 * log(x / y).
y^(1/3) is the same thing as cube root of y.
here's my worksheet.
some comments before you view it.
log(x) - log(y) - log(z) = log(x/y) - log(z) = log((x/y)/z)
a * log(x) = log(x^a)
x^a/x^b = x^(a-b)
x^-a - 1/x^a
(x/y)^a = x^a/y^a
(x*y)^a = x^a*y^a
you'll see these concepts being utilized in the worksheet below.
if you have any specific questions after going through the worksheet, feel free to ask and i'll be glad to provide additional explanations as necessary.
in the meantime, here's a reference you might find helpful. https://www.purplemath.com/modules/logrules.htm
