Question 8 ~ of 21 Step 1 of 1
Use the properties of logarithms to write the following expression as a single term that doesn’t contain a logarithm.

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Question 8 ~ of 21 Step 1 of 1 Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm. $$ e^{7-7 \ln (x)+\ln (y)} $$

UpStudy AI · Accepted Answer

1. Write the original expression:
   $$
   e^{7-7 \ln(x)+\ln(y)}
   $$

2. Use the property $$ e^{A+B+C} = e^A \cdot e^B \cdot e^C $$:
   $$
   e^{7-7 \ln(x)+\ln(y)} = e^7 \cdot e^{-7 \ln(x)} \cdot e^{\ln(y)}
   $$

3. Apply the inverse property $$ e^{\ln(a)} = a $$ for the terms:
   $$
   e^{-7 \ln(x)} = x^{-7} \quad \text{and} \quad e^{\ln(y)} = y
   $$

4. Combining the results:
   $$
   e^7 \cdot x^{-7} \cdot y = \frac{e^7 y}{x^7}
   $$

The expression as a single term is:
$$
\frac{e^7 y}{x^7}
$$
The expression simplifies to $$ \frac{e^7 y}{x^7} $$.

Question 8 ~ of 21 Step 1 of 1
Use the properties of logarithms to write the following expression as a single term that doesn’t contain a logarithm.

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Question 8 ~ of 21 Step 1 of 1 Use the properties of logarithms to write the following expression as a single term that doesn’t contain a logarithm.

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Question 8 ~ of 21 Step 1 of 1
Use the properties of logarithms to write the following expression as a single term that doesn’t contain a logarithm.