A number in front of a logarithm can go up as a power. These free printable worksheets practice that one law on its own, turning 3 log₂ 3 into log₂ 27 and 2 log 12 into log 144.
If they get stuck
The answer key prints on a separate page.
The move is short, and the mistake is multiplying where the power belongs. 3 log₂ 3 is log₂ 27, because 3³ is 27, and a student who multiplies gets log₂ 9. The reason is the same as the rest of this family: a logarithm is an exponent, and multiplying an exponent raises the power.
This law is the one that matters most later on. It is how an unknown exponent gets brought down so an exponential equation can be solved, and that step only feels natural to a student who has already moved numbers in this direction. Here they go up; in that equation they come down.
3 log₁₀ 3