Advertisements
Advertisements
प्रश्न
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
उत्तर
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
संबंधित प्रश्न
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
Assuming that x, y, z are positive real numbers, simplify the following:
`root5(243x^10y^5z^10)`
Find the value of x in the following:
`(3/5)^x(5/3)^(2x)=125/27`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
If \[8^{x + 1}\] = 64 , what is the value of \[3^{2x + 1}\] ?
The value of 64-1/3 (641/3-642/3), is
If x = \[\sqrt[3]{2 + \sqrt{3}}\] , then \[x^3 + \frac{1}{x^3} =\]
Simplify:
`7^(1/2) . 8^(1/2)`
