logarytmy xxx: (log(35−x³) / (log (5−x) > 3

M:

Jolanta:

log(35−x3
	>3.
log(5−x)

35−x³*>0 x³<35 x<³√35 5−x>0. x<5 x(−∞ ,³√35) log_5−x(35−x³) >3 log_5−x(35−x³) >log_5−x(5−x)³ 35−x³>(5−x)³. (a³−3a²b+3ab²−b³ 35−x³>125−75x+15x²−x³ 0>15x²−75x+90 /:15 x²−5x+6 <0 Δ=25−24=1

	−b−√Δ		5−1
x1=		=		=2
	2a		2

	5+1
x2=		=3
	2

x²−5x+6<0. dla x∊(2;3)