If log10 a=x and log10 b=y. Express log10 [100a³b^(-1/2) ÷b²] in terms of x and y
The expression 2+3x-5/2y cannot be simplified any further because there are no like terms to combine. Therefore, this is the final answer.
Using log rules:
log10 [100a³b^(-1/2) ÷b²]
= log10 (100a³) + log10 (b^(-1/2)) - log10 (b²)
= 2log10(a) + (-1/2)log10(b) - 2log10(b)
= 2x - (5/2)y
2+3x-5/2 y
To express log10 [100a³b^(-1/2) ÷ b²] in terms of x and y, we can use logarithmic properties and rules. Let's break it down step by step:
1. Start with the logarithmic expression:
log10 [100a³b^(-1/2) ÷ b²]
2. Apply the rules of logarithms:
log10 (100) + log10 (a³) + log10 (b^(-1/2)) - log10 (b²)
3. Simplify each logarithmic term:
log10 (100) = log10 (10^2) = 2
log10 (a³) = 3 log10 (a)
log10 (b^(-1/2)) = -1/2 log10 (b)
log10 (b²) = 2 log10 (b)
4. Substitute the given expressions:
2 + 3 log10 (a) - (1/2) log10 (b) - 2 log10 (b)
5. Combine like terms:
2 - 2 log10 (b) + 3 log10 (a) - (1/2) log10 (b)
6. Rewrite in terms of x and y:
2 - 2y + 3x - (1/2)y
The final expression for log10 [100a³b^(-1/2) ÷ b²] in terms of x and y is 2 - 2y + 3x - (1/2)y.