Page 32 - Standard Handbook Of Petroleum & Natural Gas Engineering

Algebra 21

a
-ox=- ax
b b
a
x
c
-*-*-=- axc
b y z byz
To divide one fraction by another, invert the divisor and multiply:

Exponents

a" = 1 (a # 0) and a' = a
a-"' = l/am

avn = and amIn =

(ab)" = a"b"
(a/b)" = a"/b"

Except in simple cases (square and cube roots) radical signs are replaced by
fractional exponents. If n is odd,

but if n is even, the nth root of -a is imaginary.

Logarithms
The logarithm of a positive number N is the power to which the base (10 or
e) must be raised to produce N. So, x = logeN means that ex = N, and x = log,,N
means that 10" = N. Logarithms to the base 10, frequently used in numerical
computation, are called common or denary logarithms, and those to base e, used
in theoretical work, are called natural logarithms and frequently notated as In.
In either case,

log(ab) = log a + log b