Advertisements
Advertisements
Question
Solve the following equation for x:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Advertisements
Solution
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
`rArr(2^2)^(x-1)xx(1/2)^(3-2x)=(1/2^3)^x`
`rArr(2^2)^(x-1)xx(2^-1)^(3-2x)=(2^-3)^x`
`rArr2^(2x-2)xx2^(2x-3)=2^(-3x)`
`rArr2^(2x-2+2x-3)=2^(-3x)`
`rArr2^(4x-5)=2^(-3x)`
⇒ 4x - 5 = -3x
⇒ 4x + 3x = 5
⇒ 7x = 5
`rArr x = 5/7`
APPEARS IN
RELATED QUESTIONS
Prove that:
`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`
Prove that:
`1/(1 + x^(b - a) + x^(c - a)) + 1/(1 + x^(a - b) + x^(c - b)) + 1/(1 + x^(b - c) + x^(a - c)) = 1`
Find the value of x in the following:
`(13)^(sqrtx)=4^4-3^4-6`
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of ` 2^(-x+4y)`.
Solve the following equation:
`3^(x-1)xx5^(2y-3)=225`
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
When simplified \[( x^{- 1} + y^{- 1} )^{- 1}\] is equal to
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
Simplify:-
`(1/3^3)^7`
