Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What is the value of [tex]\log_6 \frac{1}{36}[/tex]?

A. [tex]-6[/tex]
B. [tex]-2[/tex]
C. [tex]2[/tex]
D. [tex]6[/tex]

Sagot :

GinnyAnswer
To solve the expression \(\log_6 \frac{1}{36}\), we need to determine the power to which the base 6 must be raised to obtain \(\frac{1}{36}\).

Firstly, let's consider \(\frac{1}{36}\) in terms of \(6\):

We know that:
[tex]\[ 36 = 6^2 \][/tex]
Therefore, \(\frac{1}{36}\) can be written as:
[tex]\[ \frac{1}{36} = \frac{1}{6^2} = 6^{-2} \][/tex]

Now, we need to find the logarithm:
[tex]\[ \log_6(6^{-2}) \][/tex]

The logarithm \(\log_b(a)\) of a number \(a\) with base \(b\) is the exponent \(x\) such that \(b^x = a\).

In our case:
[tex]\[ \log_6(6^{-2}) = -2 \][/tex]

Thus, the value of \(\log_6 \frac{1}{36}\) is \(-2\).

So, the correct answer is:
[tex]\[\boxed{-2}\][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.