Firstly, the y values of the line and curve will intercept. y = mx = e^3x.
Now the gradients of the line and the tangent will intercept, m = 3e^3x.
Combine the two equations, m = 3mx, x = 1/3.
Therefore since mx = e^3x, now when x = 1/3,
m(1/3) =e^3(1/3)
m/3 = e^1
m = 3e