1. **State the problem:** Solve the equation $$\log_{12}(k - 10) + 5 = 4$$ for $k$. 2. **Isolate the logarithmic term:** Subtract 5 from both sides: $$\log_{12}(k - 10) = 4 - 5 = -1$$ 3. **Rewrite the logarithmic equation in exponential form:** Recall that if $$\log_a b = c$$ then $$b = a^c$$. So, $$k - 10 = 12^{-1}$$ 4. **Evaluate the exponential:** $$12^{-1} = \frac{1}{12}$$ 5. **Solve for $k$:** $$k = 10 + \frac{1}{12} = \frac{120}{12} + \frac{1}{12} = \frac{121}{12}$$ 6. **Final answer:** $$k = \frac{121}{12}$$