已知x>1,y>1,z>1,log(x)W=24,log(y)W=40,log(xyz)W=12求log(z)W

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已知x>1,y>1,z>1,log(x)W=24,log(y)W=40,log(xyz)W=12求log(z)W

已知x>1,y>1,z>1,log(x)W=24,log(y)W=40,log(xyz)W=12求log(z)W
已知x>1,y>1,z>1,log(x)W=24,log(y)W=40,log(xyz)W=12求log(z)W

已知x>1,y>1,z>1,log(x)W=24,log(y)W=40,log(xyz)W=12求log(z)W
60
log(x)W=lgW/lgx = 24 lgx=lgW/24
log(y)W=40=lgW/lgy lgy=lgW/40
log(xyz)W=12=lgW/(lgx+lgy+lgz) so lgz= lgW/60
so log(z)W=60

用换底公式把底数与真数换位,再用减法,合并成真数除法,在换底倒会即可

log(x)W=24---log(W)x=1/24
log(y)W=40----log(W)y=1/40
log(xyz)W=12----log(W)xyz=1/12
log(W)z=log(W)xyz-log(W)x-log(W)y=1/60
log(z)W=60

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