https://file.aiquickdraw.com/mathbot/file/1726447314009yv8is1u4.jpg

Let's solve the two logarithmic expressions shown in the image:

1. **log 10:**
   This is a base-10 logarithm. When no base is specified in a logarithmic expression, the base is assumed to be 10.

   Using the logarithmic rule:
   \[
   \log_b(b^x) = x
   \]
   Since \(\log_{10}(10)\), the base and the number are both 10, the result is:
   \[
   \log 10 = 1
   \]

2. **ln \(e^3\):**
   The natural logarithm (ln) is the logarithm to the base \(e\). Using the property:
   \[
   \ln(e^x) = x
   \]
   Since \(e^3\) is the input, the result is:
   \[
   \ln(e^3) = 3
   \]

### Final answers:
1. \(\log 10 = 1\)
2. \(\ln e^3 = 3\)

Would you like any more details or explanations?

Here are some related questions:
1. What is the value of \(\log 100\)?
2. How do you simplify \(\ln(e^{2x})\)?
3. What is the result of \(\log_b(b^x)\) in general form?
4. How do you solve \(\log_2(8)\)?
5. What is the base of the natural logarithm?

**Tip:** Remember, the logarithmic and exponential functions are inverses of each other. This makes simplifying expressions involving \(\ln\) and \(\log\) straightforward when their bases match!

Find the value of the following logarithmic expressions: log 10 and ln e^3.

Learn how to solve logarithmic expressions like log 10 and ln e^3 using key logarithmic properties and formulas. Suitable for students in Grades 9-11.

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