高一对数的练习已知log23=a,log35=b,用a,b来表示log1520已知log627=a,用a表示log1816

Question

高一对数的练习
已知log23=a,log35=b,用a,b来表示log15 20
已知log6 27=a,用a表示log18 16

Answer 1

log15 20
=log15 4*5
=log15 4+log15 5
=2*(log15 2)+log15 5
=2/(log2 15)+1/(log5 15)
=2/(log2 3+log2 5)+1/(log5 5+log5 3)
=2/(log2 3+(log3 5)*(log2 3))+1/(1+1/(log3 5))
=2/(a+a*b)+1(1+1/b)
=(2+a*b)/(a+a*b)
a=log6 27=3*(log6 3)=3/(log3 6)=3/(1+log3 2)=3/(1+1/(log2 3))
log2 3=a/(a-3)
log18 16=4*(log18 2)=4/(log2 18)=4/(1+2*(log2 3))
=(4a-12)/(3a-3)