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A logarithm is quite the opposite of an exponential function.
Whereas an exponential is y=ax , a log is logay=x
For example, log39=2 because you raise 3 by the 2nd power to get 9. In other words, log39=2 because 32=9
Logarithms are present because they are a handy way to solve exponential equations, and because calculators use them to great advantage.
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ProfessorPretty much, yeah. It's just another way of expressing exponents.
Say you know the following: (we'll start off easily)
16 = 42
You could also write that as:
log4 16 = 2
Algebraically,
a = bc
so,
logb a = c (b is known as the base, so it is read: log base b of a equals c)
Also, logb a = (log a) / (log b)
A logarithm is the inverse of exponentiation; that is, the log of a number is the exponent to which its base is raised to produce that number. For example common logarithms have base 10; the value N of the log of a number x is found as 10 to the N exponent equals x. For example the log 20 = N; 10 to the N exponent = 20; N = 1.301
Yes, sort of. Asking for the logarithm is equivalent to asking for an unknown exponent. Using the common (base-10) logarithms:Let's assume that somebody asks for log(10) 1000. (The 10 is supposed to be in subscript.)
This is equivalent to asking to complete for "x" in the following equation:
10 to the power x = 1000
(In this case, the answer is 3.)
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What is the application of logarithm and anti logarithm?
The main use for a logarithm is to find an exponent. If N = a^x Then if we are told to find that exponent of the base (b) that will equal that value of N then the notation is: log N ....b And the result is x = log N ..........b Such that b^x = N N is often just called the "Number", but it is the actuall value of the indicated power. b is the base (of the indicated power), and x is the exponent (of the indicated power). We see that the main use of a logarithm function is to find an exponent. The main use for the antilog function is to find the value of N given the base (b) and the exponent (x)
Why log 0 is minus infinity?
The logarithm of zero is defined as approaching negative infinity because logarithmic functions represent the exponent to which a base must be raised to produce a given number. As the input to the logarithm approaches zero from the positive side, the exponent needed to achieve that value becomes increasingly negative. Therefore, ( \log_b(0) ) tends toward negative infinity, indicating that no finite exponent can result in zero when using positive bases.
What is a logarithm normally used for?
The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. THere are seven main applications that logarithms are used for including psychology, computational complexity, fractals, music, and number theory.
Are negative and inverse relationships the same?
Not necessarily. Negatives are called opposites, or additive inverses. Inverses is much more general. For example, the inverse of an exponent is a logarithm.
Find the inverse log of negative 3.1?
The inverse of the logarithm of a number is ten to the number, meaning that the number is the exponent. In this case, 10^-3.1 equals approximately .0007943.
