Answer:
Choice 3
[tex]log \frac{x^2y}{z^2}[/tex]
Step-by-step explanation:
We use 3 of the rules of logarithms
[tex]\log (ab) = \log a + \log b[/tex]
[tex]\log\frac{a}{b} = \log a - \log b[/tex]
[tex]\log (a^n) = n\log a[/tex]
[tex]\log\frac{x^2y}{z^2} =\ log(x^2y) - \log(z^2)[/tex] (quotient rule)
[tex]\log(x^2y) = \log x^2 + \log y[/tex] (product rule)
[tex]\log x^2 = 2\log x[/tex] (power rule)
[tex]\log z^2 = 2\log z[/tex] (power rule)
Final result
[tex]log \frac{x^2y}{z^2} = 2\log x + \log y - \log z[/tex]
