Question

Is there an error in the work and is the answer extraneous? if so why?​

Answer 1

Answer:

x = 4

Step-by-step 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.