Question

Determine a sulucao da esquacao log2 (x-2)+ log2(x-3)=1+log2(2x-7)

Answer 1

log(2)[(x-2)(x-3)] = log(2)2+log(2)(2x-7)
log(2)(x²-5x+6) = log(2)[2.(2x-7)]
x²-6x+6 = 4x-14
x²-6x-4x+6+14 = 0
x²-10x+20 = 0
/\ = 100 - 80
/\ = 20
x = (-(-6)+/-2\/5)/2
x = (6+/-2\/5)/2
x' = (6+2\/5)/2 = 3+\/5
x" = (6-2\/2)/2 = 3-\/5

Answer 2

Log2(x-2)(x-3)=log2(2)(2x-7) x^2-3x-2x+6=4x-14 x^2-5x-4x+6+14=0 x^2-9x+20=0 ∆=81-80=1 x'=(9+1)/2=5 x"=(9-1)/2=4