Question

I need help with a problem. we are working on logs and the rules with the exponents and I can't figure it out. my problem will be attached.

Answer 1

rules are,
1. ln(ab) = ln(a) + ln(b)
2. ln(a^b) = b*ln(a) for a>0

Answer 2

and surely sqrt(a) = a^(1/2) for a>0
and (a^m)^n=a^(mn)

Answer 3

\[\ln x^9 \sqrt{\frac{ y^5 }{ z^{10} }} =\ln x^9y^{2.5}z^{-5}= \ln x^9 + \ln y^{2.5} + \ln z^{-5} = 9lnx + 2.5lny + 5lnz\]

Answer 4

thank you so much!