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Match each logarithm to its value.

A. [tex]\(\log_2 3\)[/tex]

Logarithm [tex]\(\square\)[/tex] is equal to -3.

B. [tex]\(\log_{81} 27\)[/tex]

Logarithm [tex]\(\square\)[/tex] is equal to [tex]\(\frac{3}{2}\)[/tex].

C. [tex]\(\log_9 27\)[/tex]

Logarithm [tex]\(\square\)[/tex] is equal to [tex]\(\frac{3}{4}\)[/tex].

D. [tex]\(\log_{\frac{1}{3}} 27\)[/tex]

Logarithm [tex]\(\square\)[/tex] is equal to [tex]\(\frac{1}{3}\)[/tex].


Sagot :

Sure, let's match each given logarithm to its respective value according to the results we have.

Given logarithms:
- [tex]\(\log_2 3\)[/tex]
- [tex]\(\log_{81} 27\)[/tex]
- [tex]\(\log_9 27\)[/tex]
- [tex]\(\log_{\frac{1}{3}} 27\)[/tex]

Given values:
- 1.5849625007211563
- 0.75
- 1.5
- -3.0

Let's match them step-by-step.

Step 1: Match [tex]\(\log_2 3\)[/tex]:
This value is 1.5849625007211563.

Step 2: Match [tex]\(\log_{81} 27\)[/tex]:
This value is 0.75.

Step 3: Match [tex]\(\log_{9} 27\)[/tex]:
This value is 1.5.

Step 4: Match [tex]\(\log_{\frac{1}{3}} 27\)[/tex]:
This value is -3.0.

Thus, the matching is as follows:

A. [tex]\(\log_2 3\)[/tex] is equal to [tex]\(1.5849625007211563\)[/tex].

B. [tex]\(\log_{81} 27\)[/tex] is equal to [tex]\(0.75\)[/tex].

C. [tex]\(\log_9 27\)[/tex] is equal to [tex]\(1.5\)[/tex].

D. [tex]\(\log_{\frac{1}{3}} 27\)[/tex] is equal to [tex]\(-3.0\)[/tex].

Therefore, the correct items to place in your options are:
- Logarithm [tex]\(D\)[/tex] is equal to -3.
- Logarithm [tex]\(C\)[/tex] is equal to [tex]\(\frac{3}{2}\)[/tex].
- Logarithm [tex]\(B\)[/tex] is equal to [tex]\(\frac{3}{4}\)[/tex].
- There is no logarithm corresponding directly to [tex]\(\frac{1}{3}\)[/tex].