If we want more clarity, we can form a table of values with some random values of x and substitute each of them in the given function to compute the y-values. So the curve would be increasing.įor domain: x + 1 > 0 ⇒ x > -1. If the base > 1, then the curve is increasing and if 0 1. So the range of f(x) is R.īefore drawing a log function graph, just have an idea of whether you get an increasing curve or decreasing curve as the answer. The range of any log function is the set of all real numbers (R)Įxample: Find the domain and range of the logarithmic function f(x) = 2 log (2x - 4) + 5.įor finding domain, set the argument of the function greater than 0 and solve for x.Īs we have seen earlier, the range of any log function is R.The domain of log function y = log x is x > 0 (or) (0, ∞).Hence, the range of a logarithmic function is the set of all real numbers. Thus, y can take the value of any real number. We can see that y can be either a positive or negative real number (or) it can be zero as well. Now, we will observe some of the y-values (outputs) of the function for different x-values (inputs). So the domain is the set of all positive real numbers. We know that log x is defined only when x > 0 (try finding log 0, log (-1), log (-2), etc using your calculator. Let us consider the basic (parent) common logarithmic function f(x) = log x (or y = log x). The logarithms can be calculated for positive whole numbers, fractions, decimals, but cannot be calculated for negative values. The logarithms are generally calculated with a base of 10, and the logarithmic value of any number can be found using a Napier logarithm table.
The exponential function of the form a x = N can be transformed into a logarithmic function log aN = x. The formula for transforming an exponential function into a logarithmic function is as follows. The logarithm counts the number of occurrences of the base in repeated multiples. Here we can use log functions to transform 2 x = 10 into logarithmic form as log 210 = x and then find the value of x. Finding the value of x in the exponential expressions 2 x = 8, 2 x = 16 is easy, but finding the value of x in 2 x = 10 is difficult. Some of the non-integral exponent values can be calculated easily with the use of logarithmic functions.
Here are some examples of logarithmic functions: Log functions include natural logarithm (ln) or common logarithm (log). It is the inverse of the exponential function a y = x. The basic logarithmic function is of the form f(x) = log ax (r) y = log ax, where a > 0. 1.ĭerivative and Integral of Logarithmic Functions Here we shall aim at knowing more about logarithmic functions, types of logarithms, the graph of the logarithmic function, and the properties of logarithms. The logarithm of any number N if interpreted as an exponential form, is the exponent to which the base of the logarithm should be raised, to obtain the number N. The exponential function a x = N is transformed to a logarithmic function log aN = x. Logarithmic functions are closely related to exponential functions and are considered as an inverse of the exponential function. It has numerous applications in astronomical and scientific calculations involving huge numbers. Logarithms were discovered in the 16 th century by John Napier a Scottish mathematician, scientist, and astronomer. The logarithmic function is an important medium of math calculations.
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