If log10 a= x and log10 b =y, express log10 [100a^(3)b^(-1/2) ÷ b^2] in terms of x and y

Answer 1

Using the rules of logarithms,

log10 [100a^(3)b^(-1/2) ÷ b^2]

= log10 (100) + log10 (a^(3)) + log10 (b^(-1/2)) - log10 (b^2)

= 2 + 3x - (1/2)y - 2y

Simplifying,

log10 [100a^(3)b^(-1/2) ÷ b^2] = 3x - (5/2)y + 2