Answer:
[tex]\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)[/tex]
Step-by-step explanation:
[tex]\log_5(\frac{9\sqrt{x}}{y^3})[/tex]
First rule I'm going to use is the quotient rule:
[tex]\log_b(\frac{m}{n})=\log_b(m)-\log_b(n)[/tex]
[tex]\log_5(9\sqrt{x})-\log_5(y^3)[/tex]
Secondly, I'm going to rewrite the radical.
[tex]\sqrt{x}=x^\frac{1}{2}[/tex]
[tex]\log_5(9x^\frac{1}{2})-\log_5(y^3)[/tex]
Third, I'm going to use the product rule on the first term:
[tex]\log_b(mn)=\log_b(m)+\log_b(n)[/tex]
[tex]\log_5(9)+\log_5(x^\frac{1}{2})-\log_5(y^3)[/tex]
Fourth, I'm going to use power rule for both of the last two terms:
[tex]\log_b(m^r)=r\log_b(m)[/tex]
[tex]\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)[/tex]
