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Simplifica la siguiente expresión logarítmica:
[tex]\[ \log (22) - \log (2) \][/tex]

Seleccione una:
a. [tex]\(\log \left(\frac{1}{11}\right)\)[/tex]
b. [tex]\(\log (11)\)[/tex]
c. [tex]\(\log \left(\frac{2}{22}\right)\)[/tex]
d. [tex]\(\log \left(\frac{10}{22}\right)\)[/tex]

Sagot :

GinnyAnswer
Para simplificar la expresión logarítmica [tex]\(\log (22) - \log (2)\)[/tex], podemos utilizar una propiedad fundamental de los logaritmos conocida como la propiedad de la resta de logaritmos. Esta propiedad establece que:

[tex]\[ \log(a) - \log(b) = \log\left(\frac{a}{b}\right) \][/tex]

Dado esto, podemos reescribir la expresión original de la siguiente manera:

[tex]\[ \log(22) - \log(2) = \log\left(\frac{22}{2}\right) \][/tex]

Ahora, simplificamos la fracción dentro del logaritmo:

[tex]\[ \frac{22}{2} = 11 \][/tex]

Por lo tanto, la expresión simplificada es:

[tex]\[ \log\left(\frac{22}{2}\right) = \log(11) \][/tex]

La opción correcta es:

b. [tex]\(\log (11)\)[/tex]
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