Question

(以二为底五的对数+以四为底0.2的对数)乘以(以五为底二的对数+以二十五为底0.5的对数)

详细解题步骤

Answer 1

以二为底五的对数+以四为底0.2的对数)乘以(以五为底二的对数+以二十五为底0.5的对数)
=(log2 5+log4 0.2)(log5 2+log25 0.5)
=(log2 5+log2 0.2/log2 4)(log5 2+log5 0.5/log5 25)
=(log2 5+log2 0.2/log2 2²)(log5 2+log5 0.5/log5 5²)
=[log2 5+log2 0.2/(2log2 2)][log5 2+log5 0.5/(2log5 5)]
=[log2 5+log2 0.2/(2*1)][log5 2+log5 0.5/(2*1)]
=[log2 5+(1/2)log2 0.2][log5 2+(1/2)log5 0.5]
=[log2 5+log2 √(0.2)][log5 2+log5 √(0.5)]
=[log2 5√(0.2)][log5 2√(0.5)]
=[log2 √(25*0.2)][log5 √(4*0.5)]
=[(1/2)log2 5][(1/2)log5 2]
=(1/4)log2 5*log5 2
=(1/4)(log5 5/log5 2)*log5 2
=(1/4)log5 5
=1/4*1
=1/4

或者：
(以二为底五的对数+以四为底0.2的对数)乘以(以五为底二的对数+以二十五为底0.5的对数)
=(log2 5+log4 0.2)(log5 2+log25 0.5)
=(log5 5/log5 2+log5 0.2/log5 4)(log5 2+log5 0.5/log5 25)
=(log5 5/log5 2+log5 0.2/log5 2²)(log5 2+log5 0.5/log5 5²)
=[log5 5/log5 2+log2 0.2/(2log5 2)][log5 2+log5 0.5/(2log5 5)]
=[log5 5/log5 2+(1/2)log2 0.2/log5 2][log5 2+(1/2)log5 0.5]
=[log5 5√(0.2)/log5 2][log5 2√(0.5)]
=[log5 √(25*0.2)/log5 2][log5 √(4*0.5)]
=[log5 √5/log5 2][log5 2√2]
=[(1/2)log5 5/log5 2][(1/2)log5 2]
=(1/4)log5 5
=1/4*1
=1/4