Advertisements
Advertisements
Question
If 2x = 3y = 12z, show that `1/z=1/y+2/x`
Advertisements
Solution
Let 2x = 3y = 12z = k
`rArr2=k^(1/x),` `3=k^(1/y),` `12=k^(1/z)`
Now,
`12=k^(1/z)`
`rArr2^2xx3=k^(1/z)`
`rArr(k^(1/x))^2xxk^(1/y)=k^(1/z)`
`rArrk^(2/x+1/y)=k^(1/z)`
`rArr2/x+1/y=1/z`
APPEARS IN
RELATED QUESTIONS
Simplify:-
`2^(2/3). 2^(1/5)`
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
Prove that:
`(64/125)^(-2/3)+1/(256/625)^(1/4)+(sqrt25/root3 64)=65/16`
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))`
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
If ax = by = cz and b2 = ac, show that `y=(2zx)/(z+x)`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
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 x-2 = 64, then x1/3+x0 =
