First, the introduction of logarithmic function
Logarithmic function lg is a common logarithm with 10 as the base. In mathematics, logarithm is the inverse of power, just as division is the reciprocal of multiplication, and vice versa. This means that the logarithm of a number is an exponent that must produce another fixed number. In a simple example, the logarithmic count factor in the multiplier.
More generally, the power operation allows any positive real number to be raised to any power, and always produces positive results, so the logarithm of any two positive real numbers b and x whose b is not equal to 1 can be calculated.
Second, introduce the domain of logarithmic function.
The domain of logarithmic function y=logax is {xèx >；; 0}, but when solving the domain of logarithmic compound function, we should not only pay attention to being greater than 0, but also pay attention to the fact that the base number is greater than 0 and not equal to 1. If the domain of function y=logx(2x- 1) is required, it must satisfy x >；; 0 and x≠ 1.
The history of logarithmic function and its relationship with exponent;
1, production history
Napier is very good at numerical calculation. He constructed the so-called logarithmic method based on a very unique idea related to particle motion, whose core idea is the connection between arithmetic progression and geometric sequence. He expounded the principle of logarithm in his 16 19 Description of Wonderful Logarithm Table, which was later called Napier Logarithm and recorded as a nap. X.
Therefore, Napier logarithm is neither a natural logarithm nor an ordinary logarithm, which is far from today's logarithm. The Swiss piccard (1552- 1632) also independently discovered logarithms, probably earlier than Napier, but published later (1620). Briggs of Britain created the ordinary logarithm in 1624.
2. Relationship with index
The general form of logarithmic function is y=㏒ax, which is actually the inverse function of exponential function. The two functions of an image symmetric about the straight line y=x are reciprocal functions, which can be expressed as x=ay. Therefore, the adjustment of a in exponential function (a >；; 0 and a≠ 1), it can be seen that the graph of logarithmic function is only the symmetric graph of exponential function graph about straight line y=x, because they are reciprocal functions.