Solve the logarithmic equation Be sure to reject any value t

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log_3 (x + 3) - log_3 (x - 3) = 4

Solution

Given that

log₃(x + 3) - log₃(x - 3) = 4

log₃(x + 3) - log₃(x - 3) = log₃(3⁴) [ since , a = log_b(b^a) ]

log₃(x + 3) - log₃(x - 3) =  log₃(81)

log₃[ (x + 3)/(x - 3) ] =   log₃(81) [ since , log_c(a) - log_c(b) = log_c(a/b) ]

  (x + 3)/(x - 3) = 81 [ since ,if log_bf(x) = log_bg(x) then f(x) = g(x) ]

      (x + 3) = 81(x - 3)

x + 3 = 81x - 243

81x - x = 3 + 243

80x = 246

x = 246/80

x = 123/40

x = 3.075