Answer:
x = 4
Explanation:
log₃[1 + log₃(2ˣ - 7)] = 1
log₃[1 + log₃(2ˣ - 7)] = log₃(3)
1 + log₃(2ˣ - 7) = 3
log₃(2ˣ - 7) = 2
log₃(2ˣ - 7) = log₃(3)²
2ˣ - 7 = 9
2ˣ = 9 + 7
2ˣ = 16
2ˣ = 2⁴
x = 4
By putting x = 4 in the original equation,
log₃[1 + log₃(2⁴ - 7)] = 1
log₃[1 + log₃(16 - 7)] = 1
log₃[1 + log₃(9)] = 1
log₃[1 + log₃(3)²] = 1
log₃[1 + 2] = 1
log₃[3] = 1
1 = 1
Therefore, x = 4 is not the extraneous solution and there is no error in your answer.