Question

-if 2 2x-1 =1/8 x-3 then find x
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Answer 1

Answer:

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Answer 2

Given,

The equation 2²ˣ⁻¹ =1/8ˣ⁻³ is given.

To find,

The value of x.

Solution,

The value of x for the given equation is 2.

We can simply find the value of x by using the laws of the exponent.

We will write 8 in terms of x so that the bases become the same on both sides.

        8 = 2*2*2

        8  = (2)³

 2²ˣ⁻¹ = 1/8ˣ⁻³

 2²ˣ⁻¹ =1/ ((2)³)ˣ⁻³       [8  = (2)³]

 2²ˣ⁻¹ = 1/ 2³ˣ⁻⁹          [(aⁿ)ᵇ = aⁿᵇ]

 2²ˣ⁻¹ = 2⁻(³ˣ⁻⁹)          [ 1/aᵇ = a⁻ᵇ]

  2²ˣ⁻¹ = 2⁻³ˣ⁺⁹

Same bases have same powers, then

 2x-1  = -3x+9

2x+3x = 9+1

      5x= 10

       x = 10/5

       x = 2

Hence, the value of x for 2²ˣ⁻¹ =1/8ˣ⁻³ is 2.