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The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logo x is read, y equals log to the base b of x, or more simply, y equals log base b of x. As with exponential functions, b > 0 and b 1.
The logarithmic form of the equation y=logo x is equivalent to the exponential form x=a. To rewrite one form in the other, keep the base the same, and switch sides with the other two values.
Consider the logarithmic function y=[log2(x+1)3]. This can be obtained by translating the parent graph y=log2(x) a couple of times. Consider the graph of the function y=log2(x). Since h=1, y=[log2(x+1)] is the translation of y=log2(x) by one unit to the left.
When graphed, the logarithmic function is similar in shape to the square root function, but with a vertical asymptote as x approaches 0 from the right. The point (1,0) is on the graph of all logarithmic functions of the form y=log bx y = l o g b x, where b is a positive real number.
Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
Algebraically, any number a raised to the zero power will equal 1, so the logarithm of any number at y = 0 is one. From this analysis, it can be concluded that as the base of a logarithmic function increases, the graph approaches the asymptote of x = 0 quicker.
Definition of logarithmic function. a function (such as y = logo x or y = LN x) that is the inverse of an exponential function (such as y = ax or y = ex) so that the independent variable appears in a logarithm.
The logarithmic function y = Logan is defined to be equivalent to the exponential equation x = a. y = Logan only under the following conditions: x = a, a > 0, and a1. It is called the logarithmic function with base a. Consider what the inverse of the exponential function means: x = a.
Working Definition of Logarithm The purpose of the inverse of a function is to tell you what x value was used when you already know the y value. So, the purpose of the logarithm is to tell you the exponent. Thus, our simple definition of a logarithm is that it is an exponent.
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