已知log(2)3=a,log(3)7=b,试用a、b表示log(14)56.

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已知log(2)3=a,log(3)7=b,试用a、b表示log(14)56.
已知log(2)3=a,log(3)7=b,试用a、b表示log(14)56.

已知log(2)3=a,log(3)7=b,试用a、b表示log(14)56.
log(2)7=log(2)3 X log(3)7 = ab 中间是乘号
log(14)56= log(14) (14 X4)
=1 + log(14) 4
= 1+ 1 / log(4)14
=1 + 2 / log(2)14
=1 + 2 / [log(2)2 + log(2)7]
=1 + 2 / [1 + log(2)7]
=1 + 2 / [1 + ab]
=[3 + ab] / [1 + ab]

log(14)56=lg56/lg14=(3lg2+lg7)/(lg2+lg7)=(3*lg3/a+lg3*b)/(lg3/a+lg3*b)=(3+ab)/(1+ab)

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