Question

If log(base4)x=2.5 and log(base Y)125=-3/2, find the numerical value of x/y, in simplest form.

Answer 1

x = (2^2)^(2.5)
x = 2^(2 * 2.5)
x = 2^5
x = 32
y^(-3/2) = 125
y^(-3) = 125^2
y^(-3) = (5^3)^2
y^(-3) = (5^2)^3
y^(-3) = 25^3
y = 25^(-1)
y = 1/25


x/y =>
32 / (1/25) =>
32 * 25 =>
800 is the simplest form of above