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witch of the following expression is equivalent to the logarithmic expression below. log(3)5/x^2

A)log(3) 5+2 log(3)x
B)log(3) 5-2 log(3)x
C)2 log(3) 5-log(3)x
D)log(3) 5+log(3)x

Respuesta :

apologiabiology
assuing you mean
[tex]log_{3}(\frac{5}{x^2})[/tex]
remember that [tex]log(\frac{a}{b})=log(a)-log(b)[/tex]
also, [tex]log(x^m)=(m)log(x)[/tex]

so
[tex]log_{3}(\frac{5}{x^2})=[/tex]
[tex]log_{3}(5)-log_{3}(x^2)=[/tex]
[tex]log_{3}(5)-2log{3}(x)[/tex]

the answer is B

Answer:  The correct option is

(B) [tex]\log_35-2\log_3x.[/tex]

Step-by-step explanation:  We are given to select the expression that is equivalent to the following logarithmic expression :

[tex]E=\log_3\dfrac{5}{x^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following properties of logarithms :

[tex](i)~\log_a\dfrac{b}{c}=\log_ab-\log_ac,\\\\(ii)~\log_ab^c=c\log_ab.[/tex]

From (i), we get

[tex]E\\\\=\log_3\dfrac{5}{x^2}\\\\\\=\log_35-\log_3x^2~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\\\=\log_35-2\log_3x.~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}][/tex]

Thus, the required equivalent expression is  [tex]\log_35-2\log_3x.[/tex]

Option (B) is CORRECT.

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