Question

Given log10 x = a, log10 y = b, Write down 10^(a+1) in terms of x. Write down 10^(2b) in terms of y. If log10 P = 2a - b, express P in terms of x and y.

Answer 1

log(x) = a, so 10^a = x.

log(y) = b, so 10^b = y.

10^(a + 1) = (10^a)(10) = 10x

10^(2b) = (10^b)^2 = y^2

log(P) = 2a - b

log(x²) = 2log(x) = 2a

log(1/y) = -log(y) = -b

log(P) = 2log(x) - log(y) = log(x²/y)

P = x²/y