1. The problem states: Solve for $z$ in the equation $\log_7 z = 3$. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$. 3. Using this definition, rewrite the equation $\log_7 z = 3$ in exponential form: $$z = 7^3$$ 4. Calculate $7^3$: $$7^3 = 7 \times 7 \times 7 = 343$$ 5. Therefore, the solution is: $$z = 343$$ This means $z$ equals 343, which is an integer.