1. We are given the function $y = \log_2(7x - 3)$ and asked to find $\frac{dy}{dx}$ at $x=1$. 2. Recall the derivative formula for logarithms with base $a$: $$\frac{d}{dx} \log_a u = \frac{1}{u \ln a} \cdot \frac{du}{dx}$$ where $u$ is a function of $x$. 3. Here, $u = 7x - 3$, so: $$\frac{du}{dx} = 7$$ 4. Applying the formula: $$\frac{dy}{dx} = \frac{1}{(7x - 3) \ln 2} \cdot 7 = \frac{7}{(7x - 3) \ln 2}$$ 5. Substitute $x=1$: $$\frac{dy}{dx}\bigg|_{x=1} = \frac{7}{(7(1) - 3) \ln 2} = \frac{7}{(7 - 3) \ln 2} = \frac{7}{4 \ln 2}$$ 6. Numerically, $\ln 2 \approx 0.693$, so: $$\frac{7}{4 \times 0.693} = \frac{7}{2.772} \approx 2.525$$ 7. Since the dropdown options are 0.7, 1.2, 1.7, and 4, none exactly matches 2.525, but the closest is 1.7 (highlighted). Possibly a misprint or approximation, but the exact derivative at $x=1$ is $\frac{7}{4 \ln 2}$. Final answer: $$\frac{dy}{dx}\bigg|_{x=1} = \frac{7}{4 \ln 2}$$