Respuesta :
correct option is B) log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w)
Step-by-step explanation:
Here we need to simplify a logarithmic expression and find which expression is equivalent to it . Let's find out:
We have ,
log Subscript 12 Baseline (StartFraction one-half Over 8 w EndFraction) or ,
⇒ [tex]Log_1_2(\frac{\frac{1}{2} }{8w} )[/tex]
We know that : [tex]Log(\frac{a}{b} )=Log(a)-Log(b)[/tex]
⇒ [tex]Log_1_2(\frac{1}{2}) - Log_1_2(8w)[/tex]
We know that : [tex]Log(ab) = Log(a)+Log(b)[/tex]
⇒ [tex]Log_1_2(\frac{1}{2}) -( Log_1_2(8)+Log_1_2(w))[/tex]
Therefore , correct option is B) log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w)
The expression that could be considered equivalent to logSubscript 12 Baseline (StartFraction one-half Over 8 w EndFraction would be:
B). log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w) or [tex]Log_{12}(\frac{1}{2}) - (Log_{12}(8) + Log_{12}(w))[/tex]
Given that,
[tex]Log_{12} (\frac{1/2}{8w} )[/tex]
Using the expression,
[tex]Log({\frac{a}{b}) = Log (a) - Log(b)[/tex]
We get,
[tex]Log_{12} (\frac{1/2}{8w} )[/tex]
[tex]= Log_{12}(\frac{1}{2}) - Log_{12} (8w)[/tex]
Using expression [tex]Log(ab) = Log(a) + Log(b)[/tex]
∵ [tex]Log_{12}(\frac{1}{2}) - (Log_{12}(8) + Log_{12}(w))[/tex]
Thus, option B is the correct answer.
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