Question

已知log8 3=a,log3 5=b,求lg 5

Answer 1

log8 3=a ==> 8^a=3

log3 5=b ==> 3^b=5

8^(ab)=5

2^(3ab)=5

∴log2 5=3ab

2^(3ab +1)=10

所以log2 10=3ab +1

∵lg 5= log10 5=(log2 5)/(log2 10)=3ab/(3ab+1)