Question

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

[AI-generated answer — Bot]

Using the properties of logarithms, we can simplify the expression inside the logarithm as follows:

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