The given equation is $2 = \log_4{16}$.

To write this in its equivalent exponential form, we use the definition of logarithms:

$\log_b{a} = c \implies b^c = a$

Here:

• $b = 4$ (the base),
• $c = 2$ (the logarithm result),
• $a = 16$ (the number).

Thus, the equivalent exponential form is:

$4^2 = 16$

Would you like further details or an explanation?

Related Questions

1. What are some properties of logarithms and their equivalent exponential forms?
2. How do you solve logarithmic equations using their exponential equivalents?
3. Can you graph the exponential function $y = 4^x$ and relate it to logarithms?
4. What are the steps to simplify logarithmic expressions with different bases?
5. How do logarithms apply to real-world exponential growth or decay problems?

Tip

Always remember: logarithms and exponents are inverse operations, making them extremely useful for solving equations involving either form!