Question

1. uporządkuj podane liczby w kolejności od najmniejszej do największej. zapisz obliczenia.
log₂½ log₅√5 log64 1 log ⅓ 27 log₃ 3

2. oblicz.
a) log₂(16×32) i log₂ 16+ log₂32
b) log₅ 125+ log₅25 i log₅(125×25)
c) log₄ 4/64 i log₄4 - log₄64
d) log√2 8/2 i log √2 8 - log√2 2
e) log₃ 9² i 2log₃ 9
f) log½ 8³ i 3 log½ 8

Answer 1

Z.1
log ⅓ 27< log₂ 1/2 < log₆₄ 1 < log₅√5 < log₃ 3,
bo -3 < -1 < 0 < 1/2 < 1
z.2
a) log₂(16*32) = log₂ 512 = 9
log₂ 16 + log₂ 32 = 4 + 5 = 9
b)
log ₅ 125 + log ₅ 25 = 3 + 2 = 5
log ₅ (125*25) = log ₅ 3125 = 5
c)
log ₄ 4/64 = log ₄ 1/16 = -2
log ₄ 4 - log₄ 64 = 1 - 3 = -2
d)
log √2 (8/2) = log √2 (4) = 4
log √2( 8 ) - log √2 (2) = 6 - 2 = 4
e)
log ₃ 9² = log₃ 81 = 4
2 log ₃ 9 = 2* 2 = 4
f)
log ½ 8³ = log ½ 512 = -9
3 log ½ 8 = 3* (-3) = -9