已知2.5x=1000,0.25y=1000,求证:1/x-1/y=1/3.
问题描述:
已知2.5x=1000,0.25y=1000,求证:
-1 x
=1 y
. 1 3
答
证明:∵2.5x=1000,0.25y=1000,
∴x=log2.51000,y=log0.251000,
∴
=log10002.5,1 x
=log10000.25,1 y
∴
-1 x
=log10002.5-log10000.25=log100010=1 y
1 3