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Logarithmic Functions

Logarithmic Functions

Given a positive number a, where a ≠ 1, and a positive number x, the logarithm to the base a of x, denoted by loga s, is defined by

y = loga x if and only if ay = x

Thus the logarithm of a number is the exponent to which we must raise the base to get the number. for example,

log2 8 = 3                      because 23 = 8,
log3 81 = 4                    because 34 = 81, and
log10 1000 = 3              because 103 = 1000.

The domain of the logarithmic function is the set of all positive real numbers and the range is the set of all real numbers. Since the logarithmic function reverses the action of the exponential function and vice versa, we as that each is the inverse of the other. The graph of y = loga x (a > 1) can be obtained by reflecting the graph of y = ax (a > 1) in the line y = x.

The two most widely used bases for logarithms are “10” and “e”, respectively.

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