1. **State the problem:** Find the equation of the tangent line to the curve $f(x) = 3^x$ at $x=1$. 2. **Find the point of tangency:** Evaluate $f(1)$ to get the $y$-coordinate. $$f(1) = 3^1 = 3$$ So the point is $(1, 3)$. 3. **Find the derivative:** The derivative of $f(x) = 3^x$ is given by $$f'(x) = 3^x \ln(3)$$ 4. **Compute the slope of the tangent line at $x=1$:** $$f'(1) = 3^1 \ln(3) = 3 \ln(3)$$ 5. **Write the equation of the tangent line:** Using point-slope form $y - y_1 = m(x - x_1)$, where $m = 3 \ln(3)$ and $(x_1, y_1) = (1, 3)$, $$y - 3 = 3 \ln(3)(x - 1)$$ 6. **Simplify the equation:** $$y = 3 \ln(3)(x - 1) + 3$$ This is the equation of the tangent line at $x=1$ for the function $f(x) = 3^x$.