Question

If (x-1)^x = (x-1)^4, find the solution. There are almost 4 solutions​

Answer 1

${(x - 1)}^{x} - {(x - 1)}^{4} = 0 \\ {(x - 1)}^{4} ( {(x - 1)}^{x - 4} - 1) = 0 \\ therefore \\ {(x - 1)}^{4} = 0 \: \: \: \: \: \: or \: \: {(x - 1)}^{x - 4} = 1 \\ x = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: \: \: is \: possible \: when \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 4 \: or \: 2\: and\: also\:for\:0$