Question

Oblicz:

a) log½ 56 - log½ 7 - 1

b) 2 + log₉ 7 - log₉ 21

c) 1 + 2log₂ 6 - log₂ 9

Answer 1

a) log½ 56 - log½ 7 - 1  = log1/2 (56 : 7)- 1 = log1/2 8 - log1/2 1/2 = log1/2 (8 : 1/2) = log1/2 16 =

log1/2 2^4 = log1/2 (1/2)^(-4) = -4

 

b) 2 + log₉ 7 - log₉ 21 = log9 9^2 + log9 7 - log9 21 = log9 (81 * 7 : 21) = log9 27 = log9 3^3 =

3 log9 3 = 3 log9 9^(1/2) = 3 * 1/2 = 3/2 = 1,5

 

c) 1 + 2log₂ 6 - log₂ 9 = log2 2 + log2 6^2 - log2 9 = log2 (2 * 6^2 : 9) = log2 (72 : 9) = log2 8 =

log2 2^3 = 3