WAEC Further Mathematics 2025 Theory — Question 10

Model answer

From 2(log₃x-1)=log₃x: 2log₃x-2=log₃x, so log₃x=2, meaning log₃(x²/9)=log₃x is consistent, giving x²-9x=0, so x=0 or x=9. Since x must be a positive integer, x=9 (x=0 is rejected as log is undefined there). For y=√x+1: when x=9, y=√9+1=4 (and the trivial case x=0 gives y=1). Solution: (x,y) = (9,4).