Question

Logarytmy pomocy :(

Answer 1

Zad1 log2≈0,3
a)log 4 =log2²=2log2≈2*0,3=0,6
b)log16=log2^4=4log2≈4*0,3≈1,2
c)log0,04=log(4/100)=log4-log100=log2²-2≈2*0,3-2≈0,6-2≈-1,.4
d)log1600=log(16*100)=log2^4+log100≈4*0,3+2≈1,2+2≈3,2
zad2              log4≈0,6              log5≈0,7
a)log25=log5²=2log5≈2*0,7≈1,4
b)log64=log4³=3log4≈3*0,6≈1,8
c)log0,64=log(64/100)=log64-log100=log4³-2≈3*0,6-2≈1,8-2≈-0,2
d)log2,5=log(25/10)=log25-log10=log5²-1≈2*0,7-1≈1,4-1≈0,4
e) log5/4=log5-log4≈0,7-0,6≈0,1
log20=log(4*5)=log4+log5≈0,6+0,7≈1,3
zad3 log₂x=0,4
a)log₂2x²=1,8
L=log₂2x²=log₂2+logx²=1+2log₂x=1+2+0,4=1,8
L=P
b)log₂16x³=5,2
L=log₂16x³=log₂16+log₂x³=log2^4+3logx=4+3*0,4=4+1,2=5,2
L=P
c)log₂x^4/2=0,6
L=log₂x^4/2=log₂x^4-log₂2=4log₂x-1=4*0,4-1=1,6-1=0,6
L=P
zad4 log₃=-1/4
a)log₃3x²=log₃3+logx²=1+2log₃x=1+2*(-1/4)=1-2/4=2/4=1/2
b)log₃9x^8=log₃9+log₃x^8=log₃3²+8log₃x=2log₃3+8*(-1/4)=3-2=1
c)log₃x^4/81=log₃x^4-log₃81=4log₃x-log₃3^4=4*(-1/4)-4=-5
d)log₃27x^6=log₃27+log₃x^6=log₃3³+6log³x=3+6(-1/4)=3-6/4=3/2
zad5p=log₂3        q=log₂5
a)log₂45=2p+q

L=log₂45=log₂(9*5)=log₂9+log₂5=log₂3²+q=2log₂3=2p+q
b)log₂75=p+2q
L=log₂75=log₂(3*25)=log₂3+log₂25=p+log₂5²=p+2log₂5=p+2q
L=P
c)log₂405=4p+q
L=log₂405=log₂(81*5)=log₂81+log₂5=log₂3^4+q=4log₂3=4q+p
L=P
zad6
logx/y +logy/x=0
L=logx/y+logy/x=logx-logy+logy-logx=0
L=P
b)logx²y²=2logx+2logy
L=logx²y²=logx²+logy²=2logx+2logy
L=P
c)logx²y-logxy²=logx-logy
L=logx²y-logxy²=log(x²y/xy²)=logx/y=logx-logy
L=P
d)logx^³y^4-logx²y³=logx+logy
L=logx^³y^4-logx²y³=log(x^4y^4/x²y³)=logxy=logx+logy
L=P
zad7
a)1,09^10
log1,09^10=10log1,09=10*0,0374=0,374
1,09^10≈10^374≈2,4
b)1,03^20
log1,03^20=20*0,0128=0,256
1,03^20≈10^0,256≈1,8
c)1,02^50
log1,02^50=50*0,0086=0,43
1,02^50≈10^0,43≈2,6
d)1,01^100
log1,01^100=100*0,0043=0,43
1,01^100≈100,43≈2,6