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4 Αυγ 2024 · A logarithmic function is the inverse of an exponential function and is defined for positive real numbers with a positive base (not equal to 1). The logarithmic function to the base b is represented as f(x) = log b (x), where x>0 and b >0.
provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics. In order to master the techniques explained here it is vital that you do plenty of practice exercises so that they become second nature.
In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.
We call the inverse of ax a x the logarithmic function with base a and denote it by loga. log a. In particular, logax = y ay = x. log a x = y a y = x. The cancellation formulas for logs are: aloga(x) =x, for every x> 0. a log a (x) = x, for every x> 0.
24 Μαΐ 2024 · The basic form of a logarithmic function is y = f(x) = log b x (0 < b ≠ 1), which is the inverse of the exponential function b y = x. The logarithmic functions can be in the form of ‘base-e-logarithm’ (natural logarithm, ‘ln’) or ‘base-10-logarithm’ (common logarithm, ‘log’). Here are some examples of logarithmic functions: f ...
6 Οκτ 2021 · The base-\(b\) logarithmic function is defined to be the inverse of the base-\(b\) exponential function. In other words, \(y = \log_{b}x\) if and only if \(b^{y} = x\) where \(b > 0\) and \(b ≠ 1\). The logarithm is actually the exponent to which the base is raised to obtain its argument.
In Section 5.3, we introduced the logarithmic functions as inverses of exponential functions and discussed a few of their functional properties from that perspective. In this section, we explore the algebraic properties of logarithms.
