Advertisements
Advertisements
Question
`(2/3)^x (3/2)^(2x)=81/16 `then x =
Options
2
3
4
1
Advertisements
Solution
We have to find value of x provided `(2/3)^x (3/2)^(2x)=81/16 `
So,
`(2/3)^x (3/2)^(2x)=81/16 `
`(2/3)^x (3/2)^(2x)= 3^4/3^4`
`(2x)/(3x) (3^(2x))/(2^(2x)) = 3^4/2^4`
`3^(2x -x)/2^(2x-x) = 3^4/2^4`
`3^x/2^x = 3^4/2^4`
Equating exponents of power we get x = 4.
APPEARS IN
RELATED QUESTIONS
Solve the following equations for x:
`3^(2x+4)+1=2.3^(x+2)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt2/sqrt3)^5(6/7)^2`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.
If x = 2 and y = 4, then \[\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =\]
If 102y = 25, then 10-y equals
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
Find:-
`32^(2/5)`
Which of the following is equal to x?
Simplify:
`(9^(1/3) xx 27^(-1/2))/(3^(1/6) xx 3^(- 2/3))`
