potęgi i logarytmy ddd: zad 1 oblicz: 25³/2 − 8⁻2/3 9¹/3 : 9⁻1/6 zad2 oblicz 2log5+log4−log10⁴ zad3) oblicz x korzystając z definicji logarytmu log₁/4x=−2 log_x2=1/4

Basia: 25^3/2 − 8^2/3 = (5²)^3/2 − (2³)^2/3 =5³ − 2² = 125−4 = 121 9^1/3:9^−1/6 = 9^{(1/3)−(−1/6)} = (3²)^(2/6)+(1/6) = (3²)^3/6 = (3²)^1/2 = 3¹ = 3 2log5+log4−log10⁴ = log5²+log4 − 4 = log(25*4) − 4 = log10²−4 = 2−4 = −2 x>0

	1		1		1
log1/4x = −2 ⇔ x−2 =		⇔		=		⇔ x2=4 ⇔ x=2
	4		x2		4

x>0 i x≠1

	1
logx2 =		⇔ x1/4 = 2 ⇔ x=24=16
	4