Question

1. Oblicz:
a) log(5)20-log(5)4=
b) log40+2log5=
c) log(2)(4+log(4)16)=

2. Oblicz x:
a) log(½)x²
b) log(3)(x²+1)
c) log(125)25=
d) log(√5)0,04=
e) log(³√2)16=
f)log(25)1/5=
g) log(7√7)49=

3. Zapisy za pomoca logarytmu rownosc
a) 4³=16
b) (√3)do potegi 8=81
c) √125=5√5

Answer 1

1. Oblicz:
a) log(5)20-log(5)4=log₅20/4=log₅5=1
b) log40+2log5==log40+log5²=log40*25=log 10³=3
c) log(2)(4+log(4)16)==log₂(4+2)=log₂6

2. Oblicz x:
a) log(½)x²=?
b) log(3)(x²+1)=?

c) log(125)25=
125do potx=25
5do pot3x=5²
3x=2
x=2/3

d) log(√5)0,04=
√5 do pot x= 1/25
1/2x=-2
x=-4
e) log(³√2)16=

2 do pot 1/3x= 2⁴
1/3x=4
x=12

f)log(25)1/5=
5 do pot 2x=5⁻¹
2x=-1
x=-1/2

g) log(7√7)49=
7do pot 1,5x =7²
1.5x=2
x=2*2/3=4/3

3. Zapisy za pomoca logarytmu rownosc
a) 4³=16
b) (√3)do potegi 8=81
c) √125=5√5

Answer 2

Zad. 1
a) log(5)20-log(5)4= log(5)20/4=log(5)5=1
c) log(2)4(4+log(4)16)= log(2)4(4+ 2log(4)4)= 2*6=12