Properties of logarithms confuse me...

Question

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

ln xyz⁵

Answer 1

Product Rule: ln(ab) = ln(a) + ln(b)

Power Rule: ln(a^b) = b * ln(a)

Using these rules, we can expand the expression as follows:

ln(xyz^5) = ln(x) + ln(yz^5)

Now, we further expand the second term:

ln(yz^5) = ln(y) + ln(z^5)

Since ln(z^5) can be simplified as 5 * ln(z), we have:

ln(xyz^5) = ln(x) + ln(y) + 5 * ln(z)

Therefore, the expression ln(xyz^5) can be expanded as the sum of ln(x), ln(y), and 5 times ln(z).

Answer 2