To solve the problem, we will match each logarithm with its corresponding value. Let's carefully go through each logarithm:
### A. [tex]\(\log_{z} 2\)[/tex]
The value of [tex]\(\log_{z} 2\)[/tex] is -3. However, none of the provided logarithms here yield a value of -3.
### B. [tex]\(\log_{81} 27\)[/tex]
This is the logarithm of 27 with base 81. The value of [tex]\(\log_{81} 27\)[/tex] is given as [tex]\(\frac{3}{2}\)[/tex].
### C. [tex]\(\log_{9} 27\)[/tex]
This is the logarithm of 27 with base 9. The value of [tex]\(\log_{9} 27\)[/tex] is also [tex]\(\frac{3}{2}\)[/tex].
### D. [tex]\(\log_{27} 3\)[/tex]
This is the logarithm of 3 with base 27. The value of [tex]\(\log_{27} 3\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
### Summary
We now have the following matches:
- B. [tex]\(\log_{81} 27\)[/tex] is equal to [tex]\(\frac{3}{2}\)[/tex].
- C. [tex]\(\log_{9} 27\)[/tex] is equal to [tex]\(\frac{3}{2}\)[/tex].
- D. [tex]\(\log_{27} 3\)[/tex] is equal to [tex]\(\frac{1}{3}\)[/tex].
### Filling in the Blanks:
- [tex]\(\log_{81} 27\)[/tex] corresponds to logarithm B and is equal to [tex]\(\frac{3}{2}\)[/tex].
- [tex]\(\log_{9} 27\)[/tex] corresponds to logarithm C and is equal to [tex]\(\frac{3}{2}\)[/tex].
- [tex]\(\log_{27} 3\)[/tex] corresponds to logarithm D and is equal to [tex]\(\frac{1}{3}\)[/tex].
