Verified answer

First, find when it does intersect the x-axis

0 = ln(1 + x / sqrt(3))

e^0 = 1 + x / sqrt(3)

1 = 1 + x/sqrt(3)

0 = x / sqrt(3)

0 = x

Now, find the derivative when x = 0

y = ln(1 + x/sqrt(3))

y' = (1/sqrt(3)) / (1 + x/sqrt(3))

y' = (1/sqrt(3)) / (1 + 0/sqrt(3))

y' = (1/sqrt(3)) / 1

y' = 1/sqrt(3)

Now, this is the slope at which the graph is hitting the x-axis. All you really have to do now is ask when tan(t) = 1/sqrt(3)

tan(t) = 1/sqrt(3)

t = pi/6 (30 degrees)