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Logarithmic Functions. Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = a. The logarithmic function y = Logan is defined to be equivalent to the exponential equation x = a.
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.
Definition. The logarithm is denoted “logo x” (pronounced as “the logarithm of x to base b” or “the base-b logarithm of x” or (most commonly) “the log, base b, of x”). In the equation y = logo x, the value y is the answer to the question “To what power must b be raised, in order to yield x?”.
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.
A logarithm is an exponent. ... A logarithm base b of a positive number x is such that: for b > 0, b 1, logo x = y if and only if by = x. The log bx is read “log base b of x”. The logarithm y is the exponent to which b must be raised to get x.
Logarithms can be used to solve exponential equations and to explore the properties of exponential functions. They will also become extremely valuable in calculus, where they will be used to calculate the slope of certain functions and the area bounded by certain curves.
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 natural logarithm has the number e (2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. ... Historically, Math scholars used logarithms to change division and multiplication problems into subtraction and addition problems, before the discovery of calculators.
logo(y) = x Whatever is inside the logarithm is called the “argument” of the log. Note that the base in both the exponential equation and the log equation (above) is “b”, but that the x and y switch sides when you switch between the two equations.
log 100 = 2. Because. 102 = 100. This is an example of a base-ten logarithm. ... log2 8 = 3. Because. 23 = 8. In general, you write log followed by the base number as a subscript. ... log. ... log a = r. ... LN. ... LN a = r.
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