Question

if (2.3)power x = (0.23) power y =1000 then find the value of x/y+y/x​

Answer 1

Answer:

5/2 or 2.5

Step-by-step explanation:

(2.3)^x = 1000

=> (23/10)^x = 10^3

=> 23^x/10^x = 10^3 -- Using law of exponent (a/b)^m = a^m/b^m

=> 23^x = 10^3 * 10^x

=> 23^x = 10^(3 + x)  -- Using law of exponent, a^m * a^n = a^(m + n)

23^x = 10^(3 + x) ~ equation (1)

(0.23)^y = 1000

=> (23/100)^y = 10^3

=> 23^y/10^2y = 10^3

=> 23^y = 10^3 * 10^2y

=> 23^y = 10^(3 + 2y) ~ equation (2)

Equating equation(1) = equation(2) we get,

10^(3 + x) = 10^(3 + 2y)

=> 3 + x = 3 + 2y

=> x = 2y

Therefore, x/y + y/x = 2y/y + y/2y

=> 2 + 1/2

=> 4 + 1/2

=> 5/2