Question

If log10 a= x and log10 b=y, express log10 [100a^(3) b^(-1/2) ÷b² in terms of x and y

Answer 1

2+3x-5/2y

Answer 2

2 + 3x - 5/2 y

Answer 3

Using the rules of logarithms, we can simplify the expression as follows:

log10 [100a^(3) b^(-1/2) ÷b²]

= log10 [100a^(3) b^(-1/2)] - log10 b²

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

= 2 + 3x - y - 2y

= 2 + 3x - 3y

Therefore, log10 [100a^(3) b^(-1/2) ÷b²] can be expressed in terms of x and y as 2 + 3x - 3y.

Answer 4

We need to first clarify whether 5/2 is being subtracted from y or is a part of the denominator. Assuming that the expression is:

2 + 3x - (5/2)y

We can express it as:

2 + 3x - 2.5y

Therefore, the expression 2 + 3x - 5/2y can be simplified to 2 + 3x - 2.5y.

Answer 5

The expression 2 + 3x - 5/2 y cannot be simplified any further without additional information or context. It is already in its simplest form.