Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Certainly! Let's analyze the logarithmic expression [tex]\(\log \left(\frac{1}{n}\right)\)[/tex].
We can use the properties of logarithms to simplify this expression. One important property of logarithms that is useful here is:
[tex]\[ \log \left(\frac{a}{b}\right) = \log a - \log b \][/tex]
In this case, we can apply this property with [tex]\(a = 1\)[/tex] and [tex]\(b = n\)[/tex]:
[tex]\[ \log \left(\frac{1}{n}\right) = \log 1 - \log n \][/tex]
Next, we need to evaluate [tex]\(\log 1\)[/tex]. It is a well-known fact that the logarithm of 1 in any base is always 0:
[tex]\[ \log 1 = 0 \][/tex]
So we substitute [tex]\(\log 1\)[/tex] with 0 in the expression:
[tex]\[ \log \left(\frac{1}{n}\right) = 0 - \log n \][/tex]
Simplifying this, we get:
[tex]\[ \log \left(\frac{1}{n}\right) = -\log n \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{-\log n} \][/tex]
So the answer to the question is option (d) [tex]\(-\log n\)[/tex].
We can use the properties of logarithms to simplify this expression. One important property of logarithms that is useful here is:
[tex]\[ \log \left(\frac{a}{b}\right) = \log a - \log b \][/tex]
In this case, we can apply this property with [tex]\(a = 1\)[/tex] and [tex]\(b = n\)[/tex]:
[tex]\[ \log \left(\frac{1}{n}\right) = \log 1 - \log n \][/tex]
Next, we need to evaluate [tex]\(\log 1\)[/tex]. It is a well-known fact that the logarithm of 1 in any base is always 0:
[tex]\[ \log 1 = 0 \][/tex]
So we substitute [tex]\(\log 1\)[/tex] with 0 in the expression:
[tex]\[ \log \left(\frac{1}{n}\right) = 0 - \log n \][/tex]
Simplifying this, we get:
[tex]\[ \log \left(\frac{1}{n}\right) = -\log n \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{-\log n} \][/tex]
So the answer to the question is option (d) [tex]\(-\log n\)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.