Question 9 of 21 Step 1 of 1
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient o

All exponents should be positive.

Ask by Ryan Howell. in the United States

Mar 30,2025

Question

Question 9 of 21 Step 1 of 1
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient o

All exponents should be positive.

Ask by Ryan Howell. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

$$
\begin{aligned}
2\log\left(x^3y^5\right) + 4\log\left(\frac{1}{x}\right) - 3\log(y)
&= \log\left((x^3y^5)^2\right) + \log\left(\left(\frac{1}{x}\right)^4\right) - \log\left(y^3\right) \
&= \log\left(x^{6}y^{10}\right) + \log\left(x^{-4}\right) - \log\left(y^3\right) \
&= \log\left(x^{6}y^{10} \cdot x^{-4}\right) - \log\left(y^3\right) \
&= \log\left(x^{6-4}y^{10}\right) - \log\left(y^3\right) \
&= \log\left(x^2y^{10}\right) - \log\left(y^3\right) \
&= \log\left(\frac{x^2y^{10}}{y^3}\right) \
&= \log\left(x^2y^{10-3}\right) \
&= \log\left(x^2y^7\right)
\end{aligned}
$$

Thus, the condensed expression is:

$$
\log\left(x^2y^7\right)
$$
The condensed expression is $$ \log(x^2 y^7) $$.

Question 9 of 21 Step 1 of 1
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient o

All exponents should be positive.

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Question 9 of 21 Step 1 of 1 Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient o All exponents should be positive.

Upstudy AI Solution

Answer

Solution

The Deep Dive

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Question 9 of 21 Step 1 of 1
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient o

All exponents should be positive.