abdultarr5
Answered

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8. Evaluate [tex]\log_3 \frac{1}{27}[/tex].

A. -1
B. -2
C. -3
D. -4

Sagot :

GinnyAnswer
To evaluate [tex]\(\log_3 \frac{1}{27}\)[/tex], we start by expressing [tex]\(\frac{1}{27}\)[/tex] as a power of 3.

First, recall that:
[tex]\[ 27 = 3^3 \][/tex]
Thus, the reciprocal of 27 is:
[tex]\[ \frac{1}{27} = \frac{1}{3^3} = 3^{-3} \][/tex]

Now, we substitute [tex]\(3^{-3}\)[/tex] into the logarithm:
[tex]\[ \log_3 \frac{1}{27} = \log_3 3^{-3} \][/tex]

We can use the property of logarithms that states [tex]\(\log_b (b^x) = x\)[/tex]. Applying this property here, we get:
[tex]\[ \log_3 3^{-3} = -3 \][/tex]

Therefore, the value of [tex]\(\log_3 \frac{1}{27}\)[/tex] is:
[tex]\[ -3 \][/tex]

The correct answer is:
[tex]\[ \boxed{-3} \][/tex]
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