$define negative exponent rule$

Define negative exponent rule how to#

If x x is a rational number, then x = p / q, x = p / q, where p p and q q are integers and b x = b p / q = b p q. If x x is a negative integer, then x = − y x = − y for some positive integer y, y, and we define b x = b − y = 1 / b y. Recall the properties of exponents: If x x is a positive integer, then we define b x = b One common example is population growth.įor example, if a population starts with P 0 P 0 individuals and then grows at an annual rate of 2 %, 2 %, its population after 1 year isįigure 1.43 Both 2 x 2 x and x 2 x 2 approach infinity as x → ∞, x → ∞, but 2 x 2 x grows more rapidly than x 2. (Note that we present alternative definitions of exponential and logarithmic functions in the chapter Applications of Integrations, and prove that the functions have the same properties with either definition.) Exponential FunctionsĮxponential functions arise in many applications.

We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number e. In this section we examine exponential and logarithmic functions. 1.5.7 Identify the hyperbolic functions, their graphs, and basic identities.

Define negative exponent rule how to#

1.5.6 Describe how to calculate a logarithm to a different base.

1.5.5 Explain the relationship between exponential and logarithmic functions.

1.5.4 Identify the form of a logarithmic function.

1.5.3 Recognize the significance of the number e.

1.5.2 Explain the difference between the graphs of x b x b and b x.

1.5.1 Identify the form of an exponential function.