Solving Exponential Equation @KasyannoEZMath

This tutorial video shows how to solve the exponential equation.

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[gelbkehlchen]

Solution:
9^(x-1)*1/27^(x-1) = 243^(x-1) ⟹
3²^(x-1)/3³^(x-1) = [3^(x-1)]^5 ⟹
3^(2x-2)/3^(3x-3) = 3^(5x-5) ⟹
3^(2x-2)*3^(3-3x) = 3^(5x-5) ⟹
3^(2x-2+3-3x) = 3^(5x-5) ⟹
3^(1-x) = 3^(5x-5) |because of the same base ⟹
1-x = 5x-5 |+x+5 ⟹
6x = 6 |/6 ⟹
x = 1

[karm]

let (x-1) = y
(3^2y) x (3^-3y) = 3^5y
3^(2y-3y) = 3^5y
2y-3y = 5y
6y = 0 y = 0
x-1 = 0
x = 1
what's wrong?