1. The problem asks to convert the logarithmic equation $\log_3 27 = 3$ into its equivalent exponential form. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$. 3. Here, the base $b$ is 3, the result $c$ is 3, and the argument $a$ is 27. 4. Using the definition, rewrite the logarithmic equation as an exponential equation: $$3^3 = 27$$ 5. This confirms the equivalence since $3^3 = 3 \times 3 \times 3 = 27$. 6. Therefore, the exponential form of $\log_3 27 = 3$ is $3^3 = 27$.