Advertisements
Advertisements
Question
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
Advertisements
Solution
Let 3x = 5y = (75)z = k
`rArr3=k^(1/x),` `5=k^(1/y),` `75=k^(1/z)`
`rArr5^2xx3=k^(1/z)`
`rArr(k^(1/y))^2xxk^(1/x)=k^(1/z)`
`rArrk^(2/y)xxk^(1/x)=k^(1/z)`
`rArrk^(2/y+1/x)=k^(1/z)`
`rArr2/y+1/x=1/z`
`rArr(2x+y)/(xy)=1/z`
`rArrz=(xy)/(2x+y)`
APPEARS IN
RELATED QUESTIONS
Prove that:
`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`
Simplify:
`(16^(-1/5))^(5/2)`
Prove that:
`9^(3/2)-3xx5^0-(1/81)^(-1/2)=15`
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Show that:
`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`
Find the value of x in the following:
`(root3 4)^(2x+1/2)=1/32`
`(2/3)^x (3/2)^(2x)=81/16 `then x =
If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =
If g = `t^(2/3) + 4t^(-1/2)`, what is the value of g when t = 64?
The simplest rationalising factor of \[\sqrt[3]{500}\] is
