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Andrew [12]
3 years ago
11

Use the properties of logarithms to expand the expression as a sum or difference, and/or constant multiple of logarithms. (Assum

e all variables are positive) ​

Mathematics
1 answer:
Alecsey [184]3 years ago
6 0

Answer:

\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)

Step-by-step explanation:

\log_5(\frac{9\sqrt{x}}{y^3})

First rule I'm going to use is the quotient rule:

\log_b(\frac{m}{n})=\log_b(m)-\log_b(n)

\log_5(9\sqrt{x})-\log_5(y^3)

Secondly, I'm going to rewrite the radical.

\sqrt{x}=x^\frac{1}{2}

\log_5(9x^\frac{1}{2})-\log_5(y^3)

Third, I'm going to use the product rule on the first term:

\log_b(mn)=\log_b(m)+\log_b(n)

\log_5(9)+\log_5(x^\frac{1}{2})-\log_5(y^3)

Fourth, I'm going to use power rule for both of the last two terms:

\log_b(m^r)=r\log_b(m)

\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)

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