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A logarithm is an exponent. The logarithm of a number
to the base b is the power to which b must be raised
to produce produce the number. Thus, suppose y = bx.
logb(y) = x
logb(bx) = x
The logarithm of a number to the base 10 is called the
common logarithm. By convention, log(N) refers to
Logarithms can be used to express any number greater than zero. Here
are some examples.
log10(1000) = 3;
log2(32) = 5;
log5(1) = 0;
log(0.01) = -2;
log(1.49) = 0.173
Since logarithms are exponents, they follow the same mathematical
rules as exponents. We illustrate these rules below.
Let x = 10log(x) and y = 10log(y)
xy = 10log(x) * 10log(y) = 10log(x) + log(y)
log(xy) = log(10log(x) * 10log(y)) = log(x) + log(y)
xr = [10log(x)]r
log(xr) = r * log(x)