log7(1/8) * (log8 (25)+log2 (5))* log5 (49) 怎么求

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log7(1/8) * (log8 (25)+log2 (5))* log5 (49) 怎么求
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log7(1/8) * (log8 (25)+log2 (5))* log5 (49) 怎么求
log7(1/8) * (log8 (25)+log2 (5))* log5 (49) 怎么求

log7(1/8) * (log8 (25)+log2 (5))* log5 (49) 怎么求
用换底公式可知 换底公式 loga b=logc b/logc a
全换成lg 也就是c=10
=lg1/8/lg7 *( lg25/lg8 +lg5/lg2) * lg49/lg5 化简掉
=-3*lg2/lg7 *( 2lg5/3lg +lg5/lg2) * 2lg7/lg5 中间的可以合并
=-3*(5/3)*2=-10

log7(1/8) =3log7(1/2)
log8 (25)=2/3log2(5)
log5 (49)=2log5 (7)
原式=3log7(1/2) *(2/3log2(5)+log2(5))*2log5(7)
=-10log7(2) *log2(5)*log5(7)
=-10