已知：以3为底10的对数为a，以6为底25的对数为b，试用a,b表示以4为底45的对数

log3(10)=a

lg10/lg3=a,-->1/lg3=a,-->lg3=1/a

log6(25)=b

lg25/lg6=b

2lg5/(lg2+lg3)=b

2lg5=b(lg2+lg3)

2(1-lg2)=blg2+blg3

2-2lg2=blg2+b/a

lg2=(2-b/a)/(2+b)=(2a-b)/(2a+ab)

log4(45)=lg45/lg4=(lg5+lg9)/2lg2=(lg5+2lg3)/2lg2

=(1-lg2+2*1/a)/2lg2

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

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

=[2a^2+a^2b-2a^2+ab+4a+2ab]/[2a(2a-b)]

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

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