What is logarithm?

definition of logarithm

Data the real numbersThe and B, positive and with The other than 1, there is a single real number x which will make the following statement true:

Thex = b

The number x in this case is known as logarithm in B at the base The. The word logarithm can be replaced by the word exponent, so we could write that x is the exponent in B at the base The.

See the representation of this definition:

logThe b = x

So we can write the following equivalence:

In the case above, the letters used represent numbers and we are interested in finding out the numerical value of the letter x. These letters receive the following names:

a is called base of the logarithm;

b is called logarithm;

x is called logarithm.

Logarithm Properties

Properties 1 to 5, set out below, are corollaries (direct consequences) of the definition of logarithms given above. Properties 6 to 8 are the propertiesoperative From logarithms. Check out:

  • O logarithm of 1, in any base, is always equal to zero, since every number raised to zero is equal to 1.

logThe 1 = 0

  • The logarithm where the logarithm and the base are equal results in 1, since every number raised to 1 is equal to itself.

logThe a = 1

  • O logarithm whose logarithmand is equal to the base, but raised to any number, has that number as a result.

logThe Them = m

  • If the logarithms of two numbers on the same base are equal, so these two numbers are equal.

logThe c = logThe d then c = d

  • When the logarithm if b in base a is an exponent of a itself, the result will be b itself.

ThelogThe B = b

  • O logarithm of the product is equal to the sum of the logarithms.

logThe (k·h) = LogThe k + LogThe H

  • O logarithm of the ratio is equal to the difference of the logarithms.

logThex = LogThe x - LogThe y
y

  • At the logarithm of a power, the exponent “falls” and is multiplied by the logarithm.

logThe km = m·LogThe k


By Luiz Paulo Moreira
Graduated in Mathematics

Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-logaritmo.htm

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