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

\[\log_{4} x = 2.5 \]

Answer 2

=> \[x = 4^{2.5}\]

Answer 3

similarly convert the other equation to exponents and take the ratio

Answer 4

log[4] x = 2.5 --> x = 4^2.5
log[y] 125 = -3/2 --> y = sqrt (125^-3)
4^2.5 = (2^2)^2.5 = 2^5 = 32
125^-3 = 1/125^3 = 1/(5^3)^3
sqrt(1/(5^3)^3) = sqrt (1/5^9) = 5^-4.5
---> x/y = 32 / 5^-4.5 --> x/y = 32 * 5^4.5

Answer 5

\[\log_{y} 125 = -\frac{3}{2} \]
\[y^{-3/2} = 125\]
\[y = 125^{-2/3}\]
\[y = \frac{1}{25}\]
From above....x = 32
--> x/y = 32*25 = 800