The Handy Math Answer Book
use today. And neither Napier nor Bürgi mentioned the concept of a logarithmic base—something that Briggs presented. By 1624 Bri ...
logaa1, because a^1 a. For example, in the equation 3^1 3, the base is 3 and the exponent is 1; the result is 3, with the co ...
What are the rulesfor combining logarithms? There are certain rules for combining logarithms. In the following cases, let abe a ...
To expand log 2 (3x) log 2 (3) log 2 (x) To expand log 2 (12/x) log 2 (12) log 2 (x) Is it possible to simplify logarithms ...
To obtain x,determine the solution for e^11 , or xis approximately 59,874.14172. And finally, check your answer (using tables o ...
What are quartic equations? Quartic equations are polynomial equations whose highest power of the unknown variable is four. Put ...
How do you divide polynomials? To divide a polynomial by a monomial, divide each term in the polynomial by the monomial (to divi ...
What is the differenceand sum of cubes? Similar to squares, there is also the difference and sum of cubes that deals with the fa ...
(x 2/3)^2 4/9 1/3 0 (x 2/3)^2 1/9 0 (add together the 4/9 1/3 by converting the denomina- tor to 9, in which 1/3 becom ...
perfect square). For example, to solve the equation x^2 3 x4 by factoring, write the equation in standard quadratic equation ...
That equals What is the discriminantof a quadratic equation? In the quadratic equation ax^2 bxc0, the value of b^2 4 acis t ...
ent variables or numbers by addition, subtraction, multiplication, or other methods. Each row and column of a given matrix must ...
A 3 by 2 (3 2) matrix: A 2 by 3 (2 3) matrix: A 4 by 4 (4 4) matrix (when the row and column dimensions are the same, it is c ...
What is the identity matrix? The identity matrix is the n-by-nmatrix that has all ones down the main diagonal and zeroes everywh ...
resent any other n-by-nmatrix. We then have AIAand IAA. This is much like the situation when using the real numbers: x 1 x ...
What is a groupin abstract algebra? A group, usually referred to as G,is a finite or infinite set of elements together with a bi ...
Rings are usually named after one or more of their investigators. But such a prac- tice usually makes understanding the properti ...
convenient form without changing its overall meaning. Today, this way of looking at logic is called Boolean algebra. (For more i ...
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GEOMETRY BEGINNINGS What is geometry? Geometry is the study of figures or objects in space—of a certain number of dimen- sions a ...
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