(10ᵃ-1)(10ᵇ-1)
=10ᵃ⁺ᵇ-10ᵃ-10ᵇ+1
≦10ᵃ⁺ᵇ-2×10^((a+b)/2) + 1

与；log₁₀( 1+√((10ᵃ-1)(10ᵇ-1)) )≦ (a+b)/2
holds if
log₁₀( 1+√(10ᵃ⁺ᵇ-2×10^((a+b)/2) + 1) )≦ (a+b)/2
iff
( 1+√(10ᵃ⁺ᵇ-2×10^((a+b)/2) + 1)≦ 10^( (a+b)/2 )
iff
1+√(x²-2x+1) ≦ x ( where x = 10^( (a+b)/2 ) )