If the base of the exponent is 1, the function remains constant. The graph becomes a horizontal line. The function fails if the base of the exponent is less than 1 and greater than 0.
The exponential function in base b is defined by
y = bˣ where b > 0 and b is a constant.
The independent variable is x and the range is real.
For example, f(x) = 3ˣ is exponential function.
Exponential Base
If f(x) = bˣ , we call "b" the exponential base. Base
must always be positive.
exponent base is 1
if f(x) is exponential with base 1 i.e. if f(x)=1ˣ
n,m∈N then f (n/m) = 1ⁿ/ᵐ= m√1ⁿ = 1
In fact, for any real number x , 1ˣ = 1, f(x)=1ˣ is a constant function f(x) = 1. For this reason, we usually don't talk much about exponential functions with base equal to 1.
To learn more about exponential function, refer:
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