Respuesta :
The options are:
[tex](A)log_{12}8-log_{12}\frac{1}{2}+log_{12}w\\(B)log_{12}\frac{1}{2}-(log_{12}8+log_{12}w)\\(C)log_{12}\frac{1}{2}-log_{12}8+log_{12}w\\(D)\frac{log_{12}\frac{1}{2}}{log_{12}8}+log_{12}w[/tex]
Answer:
[tex][B] log_{12}\frac{1}{2}- (log_{12}8+ log_{12}w).[/tex]
Step-by-step explanation:
Given the expression:
[tex]log_{12}\dfrac{\frac{1}{2}}{8w}[/tex]
Step 1: Apply the division law of logarithm
[tex]log_{x}\dfrac{a}{b}= log_x}a- log_{x}b[/tex]
Therefore:
[tex]log_{12}\dfrac{\frac{1}{2}}{8w}= log_{12}\frac{1}{2}- log_{12}{8w}[/tex]
STEP 2:Apply the multiplication law of logarithm.
[tex]log_{x}ab= log_{x}a+ log_{x}b[/tex]
Therefore:
[tex]log_{12}{8w}= log_{12}8+ log_{12}w[/tex]
STEP 3: Substitute the result from step 2 into the result from step 1
[tex]log_{12}\dfrac{\frac{1}{2}}{8w}= log_{12}\frac{1}{2}- (log_{12}8+ log_{12}w).[/tex]
The correct option is B.
Answer: B ON EDG 2021
Step-by-step explanation:
Easy work :)
