Mathematics
Solve the following equation for x:
log6 (x - 2)(x + 3) = 1
Logarithms
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Answer
Given,
⇒ log6 (x - 2)(x + 3) = 1
⇒ (x - 2)(x + 3) = 61
⇒ (x2 + 3x - 2x - 6) = 6
⇒ x2 + x - 6 = 6
⇒ x2 + x - 12 = 0
⇒ x2 + 4x - 3x - 12 = 0
⇒ x(x + 4) - 3(x + 4) = 0
⇒ (x - 3)(x + 4) = 0
⇒ x - 3 = 0 or x + 4 = 0
⇒ x = 3 or x = -4.
Hence, x = 3, -4.
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