What made you want to look up logarithmic function? It has a useful property to find the log of a fraction by applying the identities. For more related articles on logarithmic function and its properties, register with BYJU’S – The Learning app and watch interactive videos. The logarithmic function is defined as For x > 0 , a > 0, and a\neq1, y= loga x if and only if x = ay Then the function is given by f(x) = loga x The base of the logarithm is a. The base of the logarithm is a. This can be read it as log base a of x. A logarithmic function is a function of the form which is read “ y equals the log of x, base b ” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1. In this article, we are going to discuss the definition and formula for the logarithmic function, rules and properties, examples in detail. The logarithmic function to the base e is called the natural logarithmic function and it is denoted by loge. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. Post the Definition of logarithmic function to Facebook, Share the Definition of logarithmic function on Twitter. The inverse of the exponential function y = ax is x = ay. Learn a new word every day. Please tell us where you read or heard it (including the quote, if possible). Example : log 30 + log 2 = log 60 Some of the properties are listed below. Its Domain is the Positive Real Numbers: (0, +∞) In mathematics, the logarithmic function is an inverse function to exponentiation. This function is written: $${\displaystyle f(x)=b^{x}.\,}$$ always intersects the x-axis at x=1 ... in other words it passes through (1,0) equals 1 when x=a, in other words it passes through (a,1) is an Injective (one-to-one) function. Multiply two numbers with the same base, then add the exponents. Can you spell these 10 commonly misspelled words? Logarithmic functions are the inverses of exponential functions. In general, the logarithmic function: is always on the positive side of (and never crosses) the y-axis. Raise an exponential expression to power and multiply the exponents. Here you are provided with some logarithmic functions example. Log 100 = 3 x 2 = 6, logb (x) = ln x / ln b or logb (x) = log10 x / log10 b, Other Important Rules of Logarithmic Function, There are also some of the logarithmic function with fractions. Your email address will not be published. “Logarithmic function.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/logarithmic%20function. We know that Mathematics and Science constantly deal with the large powers of numbers, logarithms are most important and useful. In Mathematics, before the discovery of calculus, many Math scholars used logarithms to change multiplication and division problems into addition and subtraction problems. By the definition, loga b = y becomes ay = b. Quotient Rule. Logarithmic Functions have some of the properties that allow you to simplify the logarithms when the input is in the form of product, quotient or the value taken to the power. 'All Intensive Purposes' or 'All Intents and Purposes'? Example : log8 56 – log8 7 = log8(56/7)=log88 = 1. The most 2 common bases used in logarithmic functions are base 10 and base e. The logarithmic function with base 10 is called the common logarithmic function and it is denoted by log10 or simply log. Use the properties of logarithms to write as a single logarithm for the given equation: 5 log9 x + 7 log9 y – 3 log9 z, By using the power rule , Logb Mp = P logb M, we can write the given equation as, 5 log9 x + 7 log9 y – 3 log9 z = log9 x5 + log9 y7 – log9 z3, From product rule, logb MN = logb M + logb N, 5 log9 x + 7 log9 y – 3 log9 z = log9 x5y7 – log9 z3, From Quotient rule, logb M/N = logb M – logb N, 5 log9 x + 7 log9 y – 3 log9 z = log9 (x5y7 / z3 ), Therefore, the single logarithm is 5 log9 x + 7 log9 y – 3 log9 z = log9 (x5y7 / z3 ), Use the properties of logarithms to write as a single logarithm for the given equation: 1/2 log2 x – 8 log2 y – 5 log2 z, 1/2 log2 x – 8 log2 y – 5 log2 z = log2 x1/2 – log2 y8 – log2 z5, 1/2 log2 x – 8 log2 y – 5 log2 z = log2 x1/2 – log2 y8z5, 1/2 log2 x – 8 log2 y – 5 log2 z = log2 (x1/2 / y8z5 ), 1/2 log2 x – 8 log2 y – 5 log2 z = \(\log _{2}\left ( \frac{\sqrt{x}}{y^{8}z^{5}} \right )\). In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8. A deeper study of logarithms requires the concept of a function. Example : log 1003 = 3. Logarithm, the exponent or power to which a base must be raised to yield a given number. The logarithmic function is defined as. If b b is any number such that b > 0 b > 0 and b ≠ 1 b ≠ 1 and x > 0 x > 0 then, y = logbx is equivalent to by =x y = log b x is equivalent to b y = x We usually read this as “log base b b of x x ”. A function is a rule that, given one number, produces another number. Here is the definition of the logarithm function. We can use a log function to find an exponent. 'Nip it in the butt' or 'Nip it in the bud'. Your email address will not be published. Test Your Knowledge - and learn some interesting things along the way. There are no restrictions on y. Definition of logarithmic function : a function (such as y = loga 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 First Known Use of logarithmic function 1836, in the meaning defined above In the same fashion, since 10 2 = 100, then 2 = log 10 100. Required fields are marked *. A logarithmic or log function is the inverse of an exponential function. Divide two numbers with the same base, subtract the exponents. 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