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

证明:∵2.5x=1000,0.25y=1000,
∴x=log2.51000,y=log0.251000,

1
x
=log10002.5,
1
y
=log10000.25,
1
x
-
1
y
=log10002.5-log10000.25=log100010=
1
3