Problem
First name
Leon
School
Hitchin Boys School
Country
Age
15
log 3 3=1
log 9 3+log 9 3=1
log 27 3+log 27 3+ log 27 3=1 answer: (3- log 27 3s)
How many log 81 3 do you need to add together to make one? answer: 4
Can we choose integers x and y so that:
log 6 x+log 6 y=1?
How many different ways are there to do this? answer: x=6 y=1, x=2 y=3, and vice versa, 2 ways
How about using log 12 ? x=12 y=1, x=3 y=4, x=6 y=2, 3 ways
How about using log 24 ? x=24 y=1, x=12 y=2, x=3 y=8, x=6 y=4, 4 ways
the number of different integers for x and y (assuming you don't just swap x and y around) is the number of factors the base has divided by 2