Question

log(3x-7) - 2log(x-1) = -1???? (na base dois, ajudem por favor, tô perdido

Answer 1

log2 (3x-7) - 2log2 (x-1) = -1

log2 (3x-7) - log2 (x-1)² = -1

log2 (3x-7)/(x-1)² = -1

(3x-7)/(x-1)² = 2-¹

(3x-7)/(x-1)² = 1/2

(x-1)² = 2(3x-7)

x²-2x+1 = 6x-14

x² -8x +15= 0

∆= 64 -60= 4 => √∆=2

x'= -b+√∆/2a = 8+2/2 = 5 ✓

x"= -b-√∆/2a = 8-2/2 = 3 ✓