Exponential and Logarithmic Functions

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Presentation transcript:

Exponential and Logarithmic Functions 1.6 Exponential and Logarithmic Functions

Exponentials Exponential functions occur when a constant (a number) is being raised to a variable power. Note that this does not necessarily include a constant raised to a transcendental function. Examples:

Properties of Exponents For positive real numbers a and b, and for real numbers x and y, the following are true:

Properties of Exponents For positive real numbers a and b, and for real numbers x and y, the following are true:

Properties of Exponential Functions The following are true:

The number e Logarithms in base e are called natural logarithms.

Natural Logarithms Let x be a positive, real number.

Properties of Natural Logs: The natural logarithm is an inverse operation to exponentiation with a base of e. Therefore, the natural log function is the inverse function to the exponential function having base e.

Properties of Logarithms Let x, y, and z be real numbers such that both x and y are non-negative. The following properties are true:

Homework Pg. 54 # 5, 7, 11, 15, 25, 27, 49, 53, 77, 83