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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.
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
Logarithms are ways to figure out what exponents you need to multiply into a specific number. For example, using the “Log” function on the number 10 would reveal that you have to multiply your base number of 10 by itself one time to equal the number 10.
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.
STEP 1: Replace the function notation f (x) by y. f (x) y. STEP 2: Switch the roles of x and y. STEP 3: Isolate the log expression on one side (left or right) of the equation. STEP 4: Convert or transform the log equation into its equivalent exponential equation.
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.
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.
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.
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.
logo() = Logan — logic. A natural logarithmic function is a logarithmic function with base e. f (x) = loges = LN x, where x > 0.
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