Question

Wiedząc,że log₃ 20=a i log₃ 15=b oblicz log₂ 360

Answer 1

Wiedząc,że log₃ 20=a i log₃ 15=b oblicz log₂ 360
log₃ 20=a
log₃ 2²*5=a→2log₃ 2+log₃ 5=a→2log₃ 2=a-(b-1)→2log₃ 2=a-b+1→log₃ 2=(a-b+1)/2
log₃ 15=b
log₃ 3*5=b
1+log₃ 5=b
log₃ 5=b-1
log₂ 360=log₂ 2³*3²*5=3log₂ 2+2log₂ 3+log₂ 5=3+2log₂ 3+log₂ 5=

3+2log₃ 3/log₃2+log₃5/log₃2=3+(2+log₃5)/log₃2=3+(2+b-1)/[(a-b+1)/2]=


3+ 2(2+b-1)/[(a-b+1)]=3+ (4+2b-2)/[(a-b+1)]=3+ (2+2b)/[(a-b+1)]=

[3(a-b+1)+ (2+2b)]/(a-b+1)=[3a-3b+3 + 2+2b]/(a-b+1)=

[3a-b+5]/(a-b+1)