Question

Logarytm iloczynu i ilorazu dwa zadania. proszę o rozwiązanie a nie sam wynik Zad.1 a) log4 2 + log4 8 =

b log 2 + log 50 =

c log1/6 3 + log1/6 2 =

d) log0,1 0,2 + log0,1 0,5=

e) log15 3+ log15 5 =

f|) log20 100 + log20 4 =

zad.2 a) log4 12- log4 3 =

b log3 18 - log3 2 =

c log6 72- log6 2 =

d log2 40 - log2 5 =

e log 1/2 3,5 - log1/2 7 =

f log1/2 6 - log1/2 3 =

Answer 1

z.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 0,1 ( 0,2) + log 0,1 (0,5) = log 0,1 ( 0,2*0,5) = log 0,1 ( 0,1) = 1 , bo 0,1^1 = 0,1

e)  log 15 (3) + log 15 (5) = log 15 ( 3*5) = log 15 (15) = 1 , bo 15^1 = 15

f)  log 20 (100) + log 20 (4 ) = log 20 ( 100*4) = log 20 ( 400) = 2,  bo 20^2 = 400

 

z.2

a)  log 4 (12) - log 4 (3) = log 4(12/3) = log 4 (4) = 1 , b0 4^1 = 4

b)  log 3 (18) - log 3 (2) = log 3 ( 18 /2) = log 3 (9 ) = 2  , bo 3^2 = 9

c)  log 6 (72) - log 6 ( 2) = log 6 ( 72 : 2) = log 6 (36) = 2 , bo 6^2 = 36

d)  log 2 ( 40) - log 2(5) = log 2 ( 40 : 5) = log 2 ( 8) = 3 ,bo 2^3 = 8

e)  log 1/2 (3,5) - log 1/2 (7) = log 1/2 ( 3,5 : 7) = log 1/2 (1/2) = 1 ,

bo (1/2)^1 = 1/2

f)  log 1/2 ( 6) - log 1/2 (3) = log 1/2 ( 6 : 3) = log 1/2 ( 2) = - 1 , bo (1/2)^(-1) = 2