Need help on these logarithimic functions thanks!!!?

Question

1. loga (a/ Square root x) - log a (square root of ax)

2. 120 (ln 5 square root x^3) + ln (3 square root of y^2) - ln (4 square root of 16z^5)0

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Btw in NUMBER 2, the 5 in the square root of x^3 goes in the left top, and the 3 and the 4 too.


thanks

Answer 1

What you mean in 2, I presume, is that you're talking about a 5th root and a 4th root and so on.

Well, in #2 the first term is 120*the logarithm of x^(3/5), and hence is 120 * 3/5 ln x = 72 lnx.

The second term is ln(y^(2/3) = 2/3 * ln y

The third term is ln ( 2 * z ^(5/4)) = ln 2 + ln (z^(5/4)) = ln 2 + 5/4 ln z.

So just add/subtract those terms together; since there are three different variables involved, there's no further simplification.