From inspection the left hand side of this equation must be less than or equal to 1, so therefore , or . So the smallest root must be greater than 149.8. I think you'll find that the root is around 160.9.
Yes, the answer is near 150 (not exactly 150, but slightly more).
You can find the solution using a numerical technique, such as Newton's method, to find the root for . It involves first making a guess as to what the root is - call it - and finding the error of this guess:
Error = ,
Then calculate the slope of f(x_1):
and set the next guess as . Iterate through this a few times and it will zero in on a value near 150.0007.