Advertisements
Advertisements
Question
If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of ` 2^(-x+4y)`.
Advertisements
Solution
It is given that `3^(4x) = (81)^-1` and `10^(1/y)=0.0001`
Now,
`3^(4x) = (81)^-1`
`rArr3^(4x)=(3^4)^(-1)`
`rArr(3^x)^4=(3^-1)^4`
`rArrx=-1`
And,
`10^(1/y)=0.0001`
`rArr10^(1/y)=1/10000`
`rArr10^(1/y)=(1/10)^4`
`rArr10^(1/y)=(10)^-4`
`rArr1/y=-4`
`rArry=-1/4`
Therefore, the value of `2^(-x+4y)` is `2^(1+4(-1/4))=2^0=1`.
APPEARS IN
RELATED QUESTIONS
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
Assuming that x, y, z are positive real numbers, simplify the following:
`sqrt(x^3y^-2)`
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
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`
Show that:
`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`
When simplified \[( x^{- 1} + y^{- 1} )^{- 1}\] is equal to
If \[8^{x + 1}\] = 64 , what is the value of \[3^{2x + 1}\] ?
When simplified \[(256) {}^{- ( 4^{- 3/2} )}\] is
The value of \[\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}\] is
