What is wrong in this solution?

Question

My teacher asks us what is wrong in the following solution:

log₃(x - 1)²=2

2log₃(x - 1) = 2

log₃(x - 1) = 1

x - 1 = 3¹ = 3

x = 4

Answer 1

You are losing a solution. Converting the log to an exponential on the first step gives you:

3² = (x - 1)²

9 = (x - 1)²

Remember that taking the square root results in both a plus and a minus answer so:

±3 = x - 1

So x = 4 or x = -2