## Ftlog r y

In the discussion of exponential functions, we emphasized that the function y = b' (with b > 1) is monotonically increasing. This means that, for any positive value of y, there is a unique exponent t (not necessarily positive) such that y = b'\ moreover, the larger the value of y, the larger must be t, as can be seen from Fig. 10.2. Translated into logarithms, the monotonicity of the exponential function implies that any positive number y must possess a unique logarithm t to a base b > 1 such that the larger the>\ the larger its logarithm. As Figs. 10.1 and 10.2

show, y is necessarily positive in the exponential function y = b'\ consequently, a negative number or zero cannot possess a logarithm.

### Common Log and Natural Log

The base of the logarithm, b > 1, does not have to be restricted to any particular number, but in actual log applications two numbers are widely chosen as basesâ€”the number 10 and the number e. When 10 is the base, the logarithm is known as common logarithm, symbolized by log10 (or if the context is clear, simply by log). With e as the base, on the other hand, the logarithm is referred to as natural logarithm and is denoted either by logt, or by In (for natural log). We may also use the symbol log (without subscript e) if it is not ambiguous in the particular context.

Common logarithms, used frequently in computational work, are exemplified by the following:

 log,,, 1000 =
0 0