Question

Wiadomo że log₂ x = 0.4 Uzasadnij że:
a) log₂2x²= 1.8
b) log₂16x³ = 5.2
c) log₂ x⁴/2 = 0.6



Wiadomo że log₃ x = - ¼. oblicz:
a) log₃3x²
b) log₃9x⁸
c) log₃ x⁴/81
d) log₃ 27 x⁶

Answer 1

A) log₂2x² = log₂2 + 2log₂x = 1 + 2 * 0,4 = 1 + 0,8 = 1,8
b) log₂16x³ = log₂16 + log₂x³ = log₂16 + 3log₂x = 4 + 3 * 0,4 = 4 + 1,2 = 5,2
c) log₂ x⁴/2 = log₂ x⁴ – log₂2 = 4log₂x – 1 = 4 * 0,4 – 1 = 1,6 – 1 = 0,6


a) log₃3x² = log₃3 + log₃x² = 1 + 2log₃x = 1 + 2 * (-¼) = 1 - ½ = ½
b) log₃9x⁸ = log₃9 + log₃x⁸ = 2 + 8log₃x = 1 + 8 * (-¼) = 1 - 2 = - 1
c) log₃ x⁴/81 = log₃x⁴ - log₃81 = 4log₃x - 4 = 4 * (-¼) - 4 = - 1 - 4 = - 5
d) log₃ 27 x⁶ = log₃27 + log₃x⁸ = 3 + 8log₃x = 3 + 8 * (-¼) = 3 - 2 = 1