Question

已知log18 5=a 18^b=3 用a b表示log45 12

Answer 1

lg12/lg5=a

lg5/lg18=b

所以2lg2+lg3=alg5=a-alg2

lg5=1-lg2=2blg3+blg2

即(2+a)lg2+lg3=a

(b+1)lg2+2blg3=1

lg2=(a-1)/(ab+b-1)

lg3=a-(a+2)(a-1)/(ab+b-1)

=(a^2b+ab-a^2-2a+2)/(ab+b-1)

lg108=2lg2+3lg3

=(3a^2b+3ab-3a^2-4a+4)/(ab+b-1)