已知log5 3=a,log5 4=b,求证:log2512=1/2(a+b)求详解

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已知log53=a,log54=b,求证:log2512=1/2(a+b)求详解已知log53=a,log54=b,求证:log2512=1/2(a+b)求详解已知log53=a,log54=b,求证

已知log5 3=a,log5 4=b,求证:log2512=1/2(a+b)求详解
已知log5 3=a,log5 4=b,求证:log2512=1/2(a+b)
求详解

已知log5 3=a,log5 4=b,求证:log2512=1/2(a+b)求详解
log5 3 = a,log5 4 = b
因此a+b = log5 3 + log5 4 = log5 (3×4) = log5 12
因此log25 12 = log 5 √12 = (1/2)(log5 12) = (1/2)(a+b)

log5(3)=a,log5(4)=b,
log25(12)=[log5(12)/log5(25)]
=(1/2)log5(12)
=(1/2)log5(3*4)
=(1/2)[log5(3)+log5(4)]
=(1/2)(a+b)