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