Write the following expression as a sum​ and/or difference of logarithms. Express powers as factors.
ln left parenthesis e x right parenthesis

To write the expression \(\ln(ex)\) as a sum and/or difference of logarithms and express powers as factors, we can use the properties of logarithms.

The properties of logarithms we will use are:
1. \(\ln(ab) = \ln(a) + \ln(b)\)
2. \(\ln(a^b) = b \cdot \ln(a)\)

Given the expression \(\ln(ex)\), we can use the first property to split it into a sum:

\[
\ln(ex) = \ln(e) + \ln(x)
\]

Since \(\ln(e) = 1\), the expression simplifies to:

\[
\ln(ex) = 1 + \ln(x)
\]

Therefore, the expression \(\ln(ex)\) written as a sum of logarithms is:

\[
\ln(ex) = 1 + \ln(x)
\]

Would you like further details or have any questions about this solution?

Here are five related questions you might want to ask:
1. How do you simplify logarithmic expressions involving products?
2. What are the rules for combining logarithms?
3. How do you use logarithm properties to expand expressions?
4. What is the natural logarithm and how is it different from other logarithms?
5. How do you solve equations involving natural logarithms?

**Tip:** Always remember to apply the properties of logarithms step-by-step to simplify or expand expressions effectively.

Learn how to write ln(ex) as a sum and/or difference of logarithms using properties of logarithms. Understand the steps involved and apply them effectively. Suitable for high school students studying logarithmic functions.

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