Here are the solutions for writing each logarithmic expression in exponential form:

1. $\log_3 x = 9$
   Exponential form:
   $x = 3^9$

2. $\log_2 8 = x$
   Exponential form:
   $8 = 2^x$

3. $\log_3 27 = x$
   Exponential form:
   $27 = 3^x$

4. $\log_4 x = 3$
   Exponential form:
   $x = 4^3$

5. $\log_2 y = 5$
   Exponential form:
   $y = 2^5$

6. $\log_5 y = 2$
   Exponential form:
   $y = 5^2$

Would you like any further details or explanations?

Here are 5 related questions:

1. How do you solve logarithmic equations like $\log_b x = y$?
2. What is the inverse relationship between logarithms and exponentials?
3. How can you apply logarithmic properties to simplify expressions?
4. What is the change of base formula for logarithms?
5. How do you solve logarithmic equations with different bases?

Tip: To convert between logarithmic and exponential forms, remember that $\log_b x = y$ means $x = b^y$.