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log2(25)乘log3(4)乘log5(9)=?

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/05 21:52:50
log2(25)乘log3(4)乘log5(9)=?
log2(25)乘log3(4)乘log5(9)
=log2(5²)乘log3(2²)乘log5(3²)
=2log2(5)乘2log3(2)乘2log5(3)
=2×2×2×[log2(5)乘log3(2)乘log5(3)]
=8
再问: log2(5)乘log3(2)乘log5(3)怎麼變形乘?再詳細點好麼?謝謝
再答: log2(5)乘log3(2)乘log5(3) =log3(5)乘log5(3) =1 利用公式loga (b) 乘logb (c)=loga (c) loga (b) 乘logb (a)=1