Final answer:
The equation y=ab^x is in exponential form with 'a' as the initial value and 'b' raised to the power of 'x'. The base 'b' can be expressed in terms of 'e' using natural logarithms, transforming the equation into y=a*e^(x*ln(b)). This represents exponential arithmetic and properties of exponents.
Step-by-step explanation:
The equation y=ab^x is already in exponential form, where a is the initial value (when x is zero), b is the base of the exponential function, and x represents the exponent. Exponential notation is a way to write numbers as a product of two terms. Here, a is the digit term, and b^x is the exponential term, where ^ indicates that b is raised to the power of x.
To express the exponential relationship with a different base, such as e (where e is approximately equal to 2.7183), you would use natural logarithms. For example, any base number b can be written as e^(ln(b)). For the equation y=ab^x, you could write b as e^(ln(b)) and then use the properties of exponents, such as e^(x*ln(b)) = (e^(ln(b)))^x = b^x, to transform the equation into y=a*e^(x*ln(b)) if necessary.