Advertisements
Advertisements
Question
If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =
Options
\[\frac{\sqrt{2}}{4}\]
\[\sqrt[2]{2}\]
4
64
Solution
For `x /(x^1.5) = 8x^-1`, we have to find the value of x.
So,
`x^1 /(x^1.5) = 8x^-1`
`x ^(1-1.5) = 8x^-1`
`x ^(-0.5) = 2^3x^-1`
`(x^0.5) /x^-1= 2^3`
`x^(-5/10) /x^-1= 2^3`
`x^(-1/2+1)= 2^3`
`x^(-1/2+2/2)= 2^3`
`x^((-1+2)/2) = 2^3`
`x^(1/2) = 2^3`
By raising both sides to the power 2 we get
`x^(1/2xx2) = 2 ^(3xx2)`
`x^(1/2xx2) = 2 ^6`
`x^1 = 64`
The value of x is 64.
APPEARS IN
RELATED QUESTIONS
Solve the following equation for x:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
Find the value of x in the following:
`(13)^(sqrtx)=4^4-3^4-6`
If a and b are different positive primes such that
`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.
State the power law of exponents.
Write the value of \[\sqrt[3]{7} \times \sqrt[3]{49} .\]
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
Which of the following is (are) not equal to \[\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}\] ?
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
If `a = 2 + sqrt(3)`, then find the value of `a - 1/a`.
