已知log8(9)=a,8(b)=6,求log54(18).
1个回答

由 log8 ( 9) = a 得 log8 (3^2) = a 即:log8 (3) = a/2

由 8^b = 6得:log8 (6) = b

所以 log54 (18) = log8 (18)/ log8 (54)

= log 8 ( 3× 6)/ log8 ( 3×3×6)

= [ log8 (3) + log 8 (6)]/[log8 (3 ) + log8 (3) + log8 (6)]

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

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

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