Question

2 log x = log (2x-3) + log (x+2)
S={?}

Answer 1

2 log x = log (2x-3) + log (x+2)

log x² = log(2x-3)(x+2) ==>   x² = (2x-3)(x+2)

2x² + 4x - 3x - 6 = x²  ==> 2x² + 4x - 3x - 6 - x² = 0

x² + x - 6 = 0

Δ = 1² - 4.1.(-6) = 1 +24 = 25

x = - 1 +/- 5      ==> x1 =  2     ;  x2 = - 3
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