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

Answer 1

Using the laws of logarithms:

log10 [ 100a^(3)b^(-2/1) ÷ b^(2) ]

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

= log10 [100] + log10 [a^(3)] - 2 log10 [b] - log10 [b^(2)]

= 2 + 3x - 2y - 2

= 3x - 2y

Answer 2

2+3x - (5/2 y)

Answer 3

We can write the given expression as:

2 + 3x - (5/2)y

Or,

2 + 3x - 2.5y

Thus, the expression 2+3x - (5/2 y) simplified is 2 + 3x - 2.5y.