LOGARITHMS The logarithm of a positive real number  'N' to the base 'b' is define as the power to which 'b' must be raised to obtain the number 'N' Thus if N = aʸ, then y = logₐN ( y>1). Note that logarithm is an inverse of indices. Example1: Simplify (a) log₁₂₅0.2 (b) log₀.₂₅16   (c) log₈0.25     Solution (a)  let log₁₂₅0.2 =                    0.2 = 125ᵐ ⇒ from definition     1/5 = 125ᵐ       5⁻¹ = 5³ᵐ        -1 = 3m         m = -1/3 (b)   let log₀.₂₅16 = k                 0.25ᵏ =16 ⇒         from definition   4⁻ᵏ = 16    4⁻ᵏ = 4²     k = -2 (c)  let log₈0.25 =m         8ᵐ = 0.25         8ᵐ = 4⁻¹          2³ᵐ = 2⁻²   ...