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:
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O logarithm of 1, in any base, is always equal to zero, since every number raised to zero is equal to 1.
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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
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "What is logarithm?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-logaritmo.htm. Accessed on June 27, 2021.
