Question

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

Answer 1

Answer:  The correct option is

(B) $\log_35-2\log_3x.$

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

$E=\log_3\dfrac{5}{x^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following properties of logarithms :

$(i)~\log_a\dfrac{b}{c}=\log_ab-\log_ac,\\\\(ii)~\log_ab^c=c\log_ab.$

From (i), we get

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

Thus, the required equivalent expression is  $\log_35-2\log_3x.$

Option (B) is CORRECT.

Answer 2

Assuing you mean
$log_{3}(\frac{5}{x^2})$
remember that $log(\frac{a}{b})=log(a)-log(b)$
also, $log(x^m)=(m)log(x)$

so
$log_{3}(\frac{5}{x^2})=$
$log_{3}(5)-log_{3}(x^2)=$
$log_{3}(5)-2log{3}(x)$

the answer is B