求log2(1\25)×log3(1\8)×log5(1\9)的值
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![求log2(1\25)×log3(1\8)×log5(1\9)的值](/uploads/image/z/613842-42-2.jpg?t=%E6%B1%82log2%281%5C25%29%C3%97log3%281%5C8%29%C3%97log5%281%5C9%29%E7%9A%84%E5%80%BC)
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求log2(1\25)×log3(1\8)×log5(1\9)的值
求log2(1\25)×log3(1\8)×log5(1\9)的值
求log2(1\25)×log3(1\8)×log5(1\9)的值
log2(1\25)×log3(1\8)×log5(1\9)
=lg(1\25)/lg2×lg(1\8)/lg3×lg(1\9)/lg5
=lg5^(-2)/lg2×lg2^(-3)/lg3×lg3^(-2)/lg5
=(-2)lg5/lg2×(-3)*lg2/lg3×(-2)*lg3/lg5
=(-2)×(-3)×(-2)
=-12