高中数学对数计算求值(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)要用简便运算啊.
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高中数学对数计算求值(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)要用简便运算啊.
高中数学对数计算
求值
(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)
要用简便运算啊.
高中数学对数计算求值(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)要用简便运算啊.
(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)
=(3*log2 5+log2 5+1/3*log2 5)*(log5 2+log5 2+log5 2)
=13/3*log2 5*3*log5 2
=13
原式=(log2 125+1/2log2 25+1/3log2 5)*(4/log2 125+2/log2 25+1/log2 5)
=(3log2 5+log2 5+1/4log2 5)*(log2 5+1/log2 5+1/log2 5)
=((13/3)*log2 5)*(3*(1/log2 5))
=3
(log2 125+log4 25+log8 5)*(log125 8+log25 4+log5 2)=(log2 125+1/2log2 25+1/3log2 5)*(1/3log5 8+1/2log5 4+log5 2)=(log2 125+log2 5+log2 5^1/3)*(log5 2+log5 2+log5 2)=log2 5^13/3*log5 2^3=13/3*3*log2 5*log5 2=13
运用对数的换底公式