I know the log rules for expanding but I am not sure how to expand these difficult ones: (also the x's here depending upon the context are multiplication)
$$\log_4(x^4yz)^2$$
$$\log_3 (((6\times 5)^2)/11)^2$$
$$\log_2(d \sqrt[3]{abc})$$
$$\log ((3\times 5)/8^3)^2$$
If you know the log rules, you also need the rules for exponents, then just apply them. For example $$\log_4(x^4yz)^2=\log_4(x^8y^2z^2)=\log_4(x^8)+\dots=8\log_4x+\dots$$ The same approach works on all the rest