Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly 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 your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.