Question

已知log9^16=a,试用a表示log6^根号24 的值

Answer 1

lg16/lg9=a

4lg2/2lg3=a

lg2=(a/2)lg3

log6(√24)

=lg√24/lg6

=1/2(lg8*3)/lg(2*3)

=1/2(lg8+lg3)/(lg2+lg3)

=1/2(3lg2+lg3)/(lg2+lg3)

=1/2[3(a/2)lg3+lg3]/[(a/2)lg3+lg3]

=(3a+2)/(2a+4)