Fundamentals of Engineering Examination Review 2001-2002 Edition

Chapter 2: Precalculus and Analytic Geometry

David R. Arterburn

ALGEBRA

Logarithms

Definition. If b is finite positive number, other than 1, and b x = N, then x is the logarithm of N to the base b, or log b N = x. If log b N = x, then b x = N.

Properties of Logarithms


Systems of Logarithms

Common (Briggsian)-base 10.

Natural (Napierian or hyperbolic)-base 2.7183 (designated by e or ?).

The abbreviation of "common logarithm" is "log," and the abbreviation of "natural logarithm" is "In."

The Solution of Algebraic Equations

The Quadratic Equation

if ax 2 + bx + c = 0, then


If b 2 ? 4 ac > 0, the roots are real and unequal; if b 2 ? 4 ac = 0, the roots are real and equal; if b 2 ? 4 ac < 0, the roots are imaginary.

Progressions

Arithmetic Progression

An arithmetic progression is a, a + d, a + 2d, a + 3d, ..., where d = common difference.

The nth term is t n = a + ( n ? 1) d

The sum of n terms is

Geometric Progression

A geometric progression is a, ar, ar 2, ar 3, ..., where r = common ratio.

The nth term is t n = ar n?1

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