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Part 1

Write the following expression as a sum​ and/or difference of logarithms. Express powers as factors.

ln left bracket e left parenthesis x plus 7 right parenthesis right bracketln[e(x+7)]

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Part 1

ln left bracket e left parenthesis x plus 7 right parenthesis right bracketln[e(x+7)]equals=enter your response here

​(Simplify your​ answer.)

To simplify the expression \(\ln[e(x+7)]\), we can apply logarithmic properties. Here’s the step-by-step breakdown:

### Step 1: Use the logarithmic property \(\ln(ab) = \ln(a) + \ln(b)\)
In this case, the expression inside the logarithm is \(e(x + 7)\), which is the product of \(e\) and \((x + 7)\). So, we can rewrite this as:
\[
\ln[e(x + 7)] = \ln(e) + \ln(x + 7)
\]

### Step 2: Simplify \(\ln(e)\)
We know that \(\ln(e) = 1\), since the natural logarithm of \(e\) is 1. Thus, the expression becomes:
\[
\ln(e) + \ln(x + 7) = 1 + \ln(x + 7)
\]

### Final Answer:
\[
\ln[e(x + 7)] = 1 + \ln(x + 7)
\]

This is the simplified form of the expression.

Would you like more details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How would the expression change if it were \(\ln[e(x - 7)]\)?
2. What happens when you have \(\ln[e^{2}(x+7)]\)?
3. Can you simplify \(\ln[a(x+7)]\) for any constant \(a\)?
4. What is the logarithmic property for dividing terms inside the logarithm?
5. How do you expand logarithms involving exponents?

**Tip**: Always remember \(\ln(e) = 1\) as it's a basic property of natural logarithms!

Write the following expression as a sum and/or difference of logarithms. Express powers as factors: ln[e(x+7)]

Learn how to simplify the expression ln[e(x+7)] by applying the product property of logarithms and recognizing that ln(e) equals 1. This problem covers essential logarithmic concepts and is suitable for students in Grades 10-12.

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