{Use of Tech} Equations of tangent lines
Find an equation of the line tangent to the given curve at a.
y = e^x; a = ln 3

Verified step by step guidance

1. Identify the function of the curve, which is given as y = e^x.
2. Determine the point of tangency by substituting a = ln(3) into the function to find the corresponding y-coordinate: y = e^(ln(3)).
3. Calculate the derivative of the function y = e^x to find the slope of the tangent line at the point of tangency.
4. Evaluate the derivative at x = ln(3) to find the slope of the tangent line at that specific point.
5. Use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope found in the previous step.