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].
