Question

已知a等于以18为底9的对数,b等于以18为底5的对数,求以36为底45的值?

Answer 1

a=log18(9)=log9(9)/log9(18)

log9(2)=1/a-1

b=log18(5)=log9(5)/log9(18)

log9(5)=b/a

log36(45)=log9(45)/log9(36)

=[log9(5) + 1]/[2log9(2) + 1]

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

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

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