यदि `a^(x)=b^(y)=c^(z)," तथा "x,y,z` गुo क्षेo में हो तो साबित कीजिए कि
`log_(b)a=log_(c)b`

Explanation

प्रश्न से `a^(x)=b^(y)=c^(z)=k` (माना)
log लेने पर `xloga=ylogb=zlogc=logk`
`:.x=(logk)/(loga),y=(logk)/(logb)" और "z=(logk)/(logc)`
`:'x,y,zG.P." में है ":.(y)/(x)=(z)/(y)`
`implies(logk)/(logb)xx(loga)/(logc)=(logk)/(logc)xx(logb)/(logk)" या "(loga)/(logb)=(logb)/(logc)`
`implieslog_(b)a=log_(c)b" "[:'(loga)/(logb)=log_(b)a]`