Fluency exercise

Logarithm lattice Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Problem

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.

$\log_{3} 2$

$\log_{4} 5$

$\log_{2} 5$

$\log_{3} 4$

$\log_{3} 5$

$\log_{5} 3$

$\log_{2} 3$

$\log_{5} 2$

$\log_{5} 4$

$\log_{4} 3$

$\log_{4} 2$

$\log_{2} 4$

You might find it helpful to think about the following questions:

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

Can you use the same logarithms to complete this grid too?

$\log_{3} 2$

$\log_{4} 5$

$\log_{2} 5$

$\log_{3} 4$

$\log_{3} 5$

$\log_{5} 3$

$\log_{2} 3$

$\log_{5} 2$

$\log_{5} 4$

$\log_{4} 3$