Question

Prosze o rozwiazanie daje naj!

Answer 1

5a]3 log 3  √2 - 1/2 log 3  2  - log 3  6=
log 3  √2³- log 3  2 do potegi 1/2- log 3  6= log 3  ( 2 √2/√2) - log 3  6= log 3  (1/3) =-1
b] log 2  0,08 +4 log 2  5- log 2  12,5= log 2 ( 0,08*5 do potegi 4 /12,5)= log 2  4=2
c] log 5  2,4 +2/3 log 5  0,125 -log 5  3= log 5  (2,4 * ∛0,125² /3)= log 5  1/5=-1
d] log 2,5-3/2 log 0,25 +log 50=log (2,5*50/√0,25³)= log1000=3
6a] log24=log6+log 36/9=log6+log36-log9=log6+log6²-log9=b+2b-a=3b-a
b] log12=log 4+log3= log 36/9+log3
skoro a=9  czyli a= log3²  czyli a=2 log 3  wiec log 3=1/2a
= log 36+log9+1/2a=2 log6+log9+1/2a=2b+a+1/2a=2b+1,5a
c] log16=log4+log4=log36/9+log36/9=log36-log9+log36-log9=2log6-log9+2log6-log9=2b-a+2b-a=4b-2a
d] log 1,5= log 6/4=log6 -log4=log6 - log 36/9=log6-log36-log9=b-2b-a=-b-a
e] log 27/4=log27-log4=log3³-log36/9=3 log3-log36-log9
skoro log3=1/2a  wiec  = 3*1/2a-2b-a=0,5a-2b
f]log 4/3=log4-log3=log36/9-1/2a=log36-log9-1/2a=2b-a-1/2a=2b-1,5a
g] log 3√2=log3+log √2=1/2a+ log2 do potegi 1/2
skoro log4=log2²=2 log2  a log 4=log36-log9=2b-a  czyli log 4=2b-a  i log4=2 log 2  wiec 2 log2=2b-a  , wiec log 2=b-1/2a
=1/2a+b-1/2a=b
h] log √3/2=log 3 do potegi 1/2 -log2= 1/2 log 3- log 2
skoro log 3=1/2a  wiec 1/2 log 3=1/4a  i log 2= b-1/2a, więc
= 1/4a-b+2/4a=3/4a-b
7]
log 600=log 6+log 10²=0,8+2=2,8
b] log 0,06= log 6-log 10²=0,8-2=-1,2
c] log 0,36=log 36 + log 10 do potegi -2=2 log 6-2=-0,4
d] log 50/3=log 100/6= log 10²-log6=2-0,8=1,2
e] log pierw. czwartego stopnia z 6= log 6 do potegi 1/4=1/4*0,8=0,2
f] log 6√10=log6+log 10 do potegi 1/2=0,8+0,5=1,3