高一数学对数与对数运算log2(25)*log3(4)*log5(9) （）里的是真数

log2(25)*log3(4)*log5(9)=2log2(5)*2log3(2)*2log5(3)=8（ln5/ln3）*（ln2/ln3）*（ln3/ln5）=8

答案是8.解法如下：
log2(25)=2*log2(5）
log3(4)=2*log3(2)
log5(9)=2*log5(3)
三个2相乘是8，后面的三个因子相乘消去了。所以是8.

vcvc

换底公式
(2lg5/lg2)(2lg2/lg3)(2lg2/lg5)
=8

log2 25*log3 4*log5 9 =log2 5^2*log3 2^2*log5 3^2 =2*log2 5*2*log3 2*2*log5 3 =8*(log2 5)*(log2 2)/(log2 3)*(log2 3)/(log2 5) =8*log2 2 =8*1 =8 或log2(25)*log3(4)*log5(9) =log25/log2 * log4/log3 * log...