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.)