We have extended one possible solution grid. Can you use other logarithms to complete the four blank cells of this grid or one based on your own solution grid?
| Increasing size \(\longrightarrow\) | |||||
|
Increasing size \(\downarrow\) |
\(\log_{\square} \square\) | ||||
| \(\log_{4} 2\) | \(\log_4 3\) | \(\log_{4} 5\) | |||
| \(\log_{\square} \square\) | \(\log_{5} 3\) | \(1\) | \(\log_{3} 5\) | \(\log_{\square} \square\) | |
| \(\log_{5} 4\) | \(\log_3 4\) | \(\log_{2} 4\) | |||
| \(\log_{\square} \square\) | |||||
Some things to think about:
- Try to make your extra logarithms as general as possible. For instance if you want \(\log_{a} 3\) to be less than \(\log_{5} 3\), what conditions must \(a\) satisfy?
- How could you include fractions or irrational numbers in your logarithms?
