How do you determine the horizontal stretch of f(x)=7^x?

You look at the coefficient of x.

If the parent function is f(x) = 7^x, there is no horizontal stretch.

If the parent function is f(x) = e^x, then your function is
.. f(x) = 7^x = (e^ln(7))^x = e^(ln(7)*x)
and the horizontal compression factor is ln(7) ≈ 1.946. (The stretch factor is 1/1.946 = 0.514.)