Question

已知log_ax=log_ac+b,求x.

Answer 1

思路分析:由于x是真數(shù),故可直接利用對(duì)數(shù)定義求解;另外,由于等式右端為兩實(shí)數(shù)和的形式,b的存在使變形產(chǎn)生困難,故可考慮將log_ac移到等式左端,或者將b變?yōu)閷?duì)數(shù)形式.

解法一:由對(duì)數(shù)定義可知:x==·a^b=c·a^b.

解法二:由已知移項(xiàng)可得log_ax-log_ac=b,

即log_a=b,由對(duì)數(shù)定義知 =a^b,

∴x=c·a^b.

解法三:∵b=log_aa^b,

∴l(xiāng)og_ax=log_ac+log_aa^b=log_ac·a^b.

∴x=c·a^b.

說(shuō)明:此題有多種解法,體現(xiàn)了基本概念和運(yùn)算性質(zhì)的靈活運(yùn)用,考查學(xué)生對(duì)于對(duì)數(shù)定義及運(yùn)算性質(zhì)的理解.