Question

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log(zy^4)

Answer 1

First,

Arrange the variables alphabetically within the expression zy^(4). This is the standard way of writing an expression.

Answer 2

log(zy^(4))

Arrange the variables alphabetically within the expression zy^(4). This is the standard way of writing an expression.
(log(y^(4)z))

The logarithm of a product is equal to the sum of the logarithms of each factor (e.g. log(xy)=log(x)+log(y)). The logarithm of a product is equal to the difference of the logarithms of each factor (e.g. log((x)/(y))=log(x)-log(y)).
(log(y^(4))+log(z))

Remove the parentheses around the expression log(y^(4))+log(z).
log(y^(4))+log(z)

The exponent of a factor inside a logarithm can be expanded to the front of the expression using the third law of logarithms. The third law of logarithms states that the logarithm of a power of x is equal to the exponent of that power times the logarithm of x (e.g. log^b(x^(n))=nlog^b(x)).
(4log(y))+log(z)

Remove the parentheses around the expression 4log(y).
4log(y)+log(z)

Answer 3

Do you understand how to work it out now?