Question

Rozwiąż równania !!! Liczę na poprawne rozwiązania !!!

a) log₄ 2+log₄ 8

b) log 2+log 50

c) log⅙ 3+log⅙ 2

d) log₁₅ 3+log₁₅ 5

e) log₄ 12-log₄ 3

f) log₃ 18-log₆ 2

g) log₆ 72-log₆ 2

h) log₂ 40-log₂ 5

i) log½ 3,5-log⅓ 7

Answer 1

a)

log 4 [2] + log 4 [ 8] = log 4 [ 2*8] = log 4 [ 16] = 2 ,  bo 4^2 = 16

b)

log 2 + log 50 = log 2*50 = log 100 = 2,  bo 10 ^2 = 100

c)

log 1/6 [ 3 ] + log 1/6 [ 2] = log 1/6 [ 3*2] = log 1/6 [6 ] = -1  , bo (1/6)^(-1) = 6

d)

log 15 [ 3] + log 15 [ 5 ] = log 15 [ 15] = 1  , bo 15^1 = 15

e)

log 4 [12 ] - log 4 [3] = log 4 [12/3] = log 4 [ 4] = 1 , bo  4^1 = 4

f)

log 3 [ 18] - log 6 [2 ] = log 3 [ 3*6] - log 6 [2] = log 3[3] + log 3[6] - log 6[2] =

= 1 + 1/ log 6 [3] - log 6 [2]

g)

log 6[72] - log 6 [2] = log 6 [ 72/2] = log 6 [ 36] = 2 ,  bo 6^2 = 36

h)

log2 [40] - log 2 [ 5 ] = log 2 [ 40/5] = log 2 [8] = 3 ,  bo 3^2 = 8

i)

log 1/2 [ 3,5] - log 1/2 [ 7] = log 1/2 [ 3,5 : 7] = log 1/2 [ 1/2] = 1, bp 1/2^(1) =1/2