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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]
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