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Thank you to everyone who submitted solutions to this problem.
Jessica form Tiffin Girls school has found a really nice way of organising all the given logarithms into a table.
This table nicely captures all the information we can get about the relative sizes of the logarithms without calculating them, by making use of the fact that $\log_b{a}$ increases in size as you increase $a$ or decrease $b$.
It also makes it much easier to read off all the different ways you could complete the given grid, of which there are quite a few. Here is one way Jessica has given to complete the grid.
You can read Jessica's full solution here .
Log Lattice
Age 16 to 18
Challenge Level 
Thank you to everyone who submitted solutions to this problem.
Jessica form Tiffin Girls school has found a really nice way of organising all the given logarithms into a table.
This table nicely captures all the information we can get about the relative sizes of the logarithms without calculating them, by making use of the fact that $\log_b{a}$ increases in size as you increase $a$ or decrease $b$.
It also makes it much easier to read off all the different ways you could complete the given grid, of which there are quite a few. Here is one way Jessica has given to complete the grid.
You can read Jessica's full solution here .
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