Question

Solve for x in the equation 2^(2x-1)x[1/8]^(1-x)=4^(3x+1)​

Answer 1

Explanation:

We have:

2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)

2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)

2^(2x-1) x 2^-3+3x = 2^6x+2

2^5x-4 = 2^6x+2

on comparing both sides we get :

5x-4 = 6x +2

x = -6

Answer 2

Answer: x=-6

Explanation:

`\displaystyle\\2^(2x-1)*((1)/(8) )^(1-x)=4^(3x+1)\\\\2^(2x-1)*8^((-1)(1-x))=(2^2)^(3x+1)\\\\2^(2x-1)*(2^3)^(x-1)=2^(2*(3x+1))\\\\2^(2x-1)*2^(3*(x-1))=2^(6x+2)\\\\2^(2x-1)*2^(3x-3)=2^(6x+2)\\\\2^(2x-1+3x-3)=2^(6x+2)\\\\2^(5x-4)=2^(6x+2)\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6`