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Log Lattice

Age 16 to 18 Challenge Level:

This resource is from Underground Mathematics.

Can you arrange some of these logarithms to complete the grid below? The values of the logarithms need to increase along the rows and down the columns. Try to do this without using a calculator.

$$ \log_{3} 2 \quad \log_{4} 5 \quad  \log_{2} 5 \quad \log_{3} 4 \quad  \log_{3} 5 \quad  \log_{5} 3 $$
$$ \log_{4} 2 \quad \log_{2} 4 \quad  \log_{2} 3 \quad \log_{5} 2 \quad \log_{5} 4 \quad  \log_{4} 3 $$

Think about
  • Can you put pairs of logarithms from the list in order of size?
  • Which logarithms are bigger than $1$ and which ones are smaller? 

This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.