Use the Laws of Logarithms to expand the expression.?

Question

log2(xy)^10

Answer 1

10log2x + 10 log2y

Answer 2

1. You have 2 terms in the log: 2 and (xy)^10
by the rule, you can separate these into addition of logs:

log 2 + log(xy)^10


2. Exponents for the term in log can be brought to the front to multiply

log 2 + 10log(xy)


3. similar to the first rule, we can separate out the x and y into addition of logs(don't forget the 10!)

log 2 + 10logx + 10logy

And there's your answer.

Another way:

1. Since the x and y in the parenthesis are being multiplied instead of added, they each carry the 10 exponent, so you can get rid of the parenthesis

log 2 * x^10 * y^10


2. Now you're ready for the Law. Separating the multiplied terms into addition of logs

log 2 + log x^10 + log y^10


3. Now you're ready for the exponent rule. In each log term with an exponent, you can bring the exponent to the front to be multiplied

log 2 + 10log x + 10log y

Answer 3

log(2)(xy)^10
10(log(2)(xy))
10(log(2)x + log(2)y)