1. The problem asks to simplify the expression $$y = 2 \ln(e^x)$$. 2. Recall the logarithm rule: $$\ln(a^b) = b \ln(a)$$. 3. Since $$\ln(e) = 1$$, we can simplify $$\ln(e^x)$$ as $$x \ln(e) = x \times 1 = x$$. 4. Substitute back into the original expression: $$y = 2 \ln(e^x) = 2 \times x = 2x$$. 5. Therefore, the simplified form is $$y = 2x$$. 6. This matches option (A). The graph points (1, 2), (2, 4) confirm the linear relationship $$y = 2x$$.