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.