若lga*lgb>lgc 能证明(10^lga)*(10^lgb)>(10^lgc)吗?

题目

若lga*lgb>lgc 能证明(10^lga)*(10^lgb)>(10^lgc)吗?

答案

反例:a = b = 10³,c = 10⁷.
lg(a)·lg(b) = 9 > 7 = lg(c).
但(10^lg(a))·(10^lg(b)) = ab = 10⁶ < 10⁷ = c = 10^lg(c).