Answer:
Option C. [tex]log_{2}\frac{1}{3}[/tex]
Step-by-step explanation:
The given logarithmic expression is [tex]\frac{log(\frac{1}{3} )}{log2}[/tex]
Rule of logarithm says
[tex]\frac{log_{e}a }{log_{e}b}=log_{b}a[/tex]
So by this rule,
expression [tex]\frac{log(\frac{1}{3} )}{log2}[/tex] will become [tex]log_{2}\frac{1}{3}[/tex]
Therefore, Option C. [tex]log_{2}\frac{1}{3}[/tex] will be the answer.
To solve the problem we must know about the rule to change the base of any logarithmic expression.
The solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
The formula which helps us to change the base of any logarithm expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca}[/tex]
Given to us
[tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]
As we have already discussed the formula for the change of the base of any logarithm expression, comparing the formula with that expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
[tex]\rm log_2\dfrac{1}{3} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
Hence, the solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
Learn more about Logarithm expression:
https://brainly.com/question/7165853
