Solve the equation Log2x3 log2 x9 4SolutionGiven equation i

Solve the equation. Log_2(x-3) + log_2 ?(x-9) =4

Solution

Given equation is

    log₂(x-3) + log₂(x-9) = 4

   log₂ (x-3)(x-9) = 4                             [ log a + log b = log ab ]

(x-3)(x-9) = 2⁴

   (x-3)(x-9) = 16

   x² - 12x + 27 = 16

   x² - 12x + 11 = 0

    x²-x-11x + 11 = 0

   x (x-1) -11 (x-1) =0

      (x-1) (x-11) = 0

        x = 1,11

Therefore,

         x = 1,11