用综合法证明(1/log519+2/log319+3/log219)
问题描述:
用综合法证明(1/log519+2/log319+3/log219)
答
用综合法证明
此题主要是把对数都换成常用对数,再求证
左边=1/log5(19)+2/log3(19)+3/log2(19)
=lg5/lg19+2lg3/lg19+3lg2/lg19
=(lg5+2lg3+3lg2)/lg19
=lg5*9*8/lg19
=lg360/lg19
右边=2=2lg19/lg19=lh19^2/lg19=lg361/lg19>lg360/lg19
所以左边