To convert the logarithmic equation $\log_{12} 144 = 2$ into exponential form, we use the definition of a logarithm:

$\log_b a = c \quad \text{is equivalent to} \quad b^c = a$

Here:

• $b = 12$ (the base),
• $c = 2$ (the logarithm value),
• $a = 144$ (the number).

So, the equation in exponential form is:

$12^2 = 144$

Let me know if you would like further details or have questions!

Related Questions:

1. What is the general definition of a logarithm and how is it related to exponential equations?
2. How can you verify the solution $12^2 = 144$?
3. What happens if the logarithmic base changes (e.g., $\log_5 25$)? How do you adjust the exponential form?
4. Can $\log_{12} (-144)$ exist? Why or why not?
5. What are the properties of logarithms (e.g., product rule, quotient rule) and how do they simplify expressions?

Tip:

Always remember: A logarithmic equation $\log_b a = c$ tells us that the base $b$ raised to the power $c$ equals $a$.