Equating exponents without a common basefrom 2x = 3x we cannot conclude anything by equating the exponents, because the bases differ.
Misreading 2x + 1the whole expression x + 1 is the exponent, not 2x + 1.
Accepting a negative value of the substitutionif y = 2x, then y is always positive.
Wrong conversion to a common base4x = 22x, not 2x.