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Question
Solve the following:
log 4 x + log 4 (x-6) = 2
Solution
log 4 x + log 4 (x-6) = 2
⇒ log 4 {x(x-6)} = 2 log 4 4
⇒ log 4 {x2 - 6x} = log 4 42
⇒ x2 - 6x = 16
⇒ x2 - 6x - 16 = 0
⇒ x2 - 8x + 2x - 16 = 0
⇒ x (x - 8) + 2 ( x - 8) = 0
⇒ (x - 8)(x + 2) = 0
⇒ x = 8 or -2
Negative value is rejected
So, x = 8.
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