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The task is to rewrite the given logarithmic and exponential expressions in a different form. Here's the breakdown:

1. **\( a^x = y \)**  
   - This is an exponential equation. In logarithmic form, it becomes:  
     \[
     \log_a y = x
     \]

2. **\( \log m^c = d \)**  
   - The logarithmic property \( \log m^c = c \log m \) can be applied here. So, it becomes:  
     \[
     c \log m = d
     \]

3. **\( \log p = q \)**  
   - This is already in logarithmic form, but in terms of an exponential form, it becomes:  
     \[
     10^q = p
     \]
   (assuming the base of the logarithm is 10)

4. **\( \log s = t \)**  
   - Similar to the above, in exponential form, this becomes:  
     \[
     10^t = s
     \]
   (again assuming the base is 10)

5. **\( \ln r = r \)**  
   - This involves the natural logarithm, where \( \ln \) is the logarithm with base \( e \). In exponential form, this becomes:  
     \[
     e^r = r
     \]

Would you like further details on any of these conversions or explanations on logarithmic/exponential properties?

Here are 5 related questions:
1. How do you convert a general logarithmic equation into its exponential form?
2. What is the base of a logarithm when it is written without specifying the base (e.g., \( \log p = q \))?
3. What is the logarithmic form of \( 2^3 = 8 \)?
4. How do properties of logarithms (such as \( \log m^c = c \log m \)) simplify complex expressions?
5. How can you apply logarithmic differentiation to solve certain calculus problems?

**Tip:** Always remember that logarithms and exponentials are inverse functions, so you can easily switch between the two forms.

Write the following statements in the form of:
1. a^x = y
2. log m^c = d
3. log p = q
4. log s = t
5. ln r = r

Learn how to convert between exponential and logarithmic forms using various mathematical concepts such as properties of logarithms. This includes examples like a^x = y, log m^c = d, and their equivalent forms. Suitable for high school students in Grades 10-12.

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