Question

An equation is shown below: 1 over 2 multiplied by x plus 3 over 2 equals 2 to the power of x What is the solution to the equation? x = 1 x = 2 x = 4 x = 8

Answer 1

x = 1

Explanation:

1/2 x 1 = 1/2

1/2 + 3/2 = 4/2 = 2

2 to the power of 1 is 2

Answer 2

First option is correct. The solution of the equation is x=1.

Explanation:

The given equation is

`(1)/(2)x+(3)/(2)=2^x`

The value of x, which satisfy the above equation is the solution of the given equation.

Put x=1 in the given equation.

`(1)/(2)(1)+(3)/(2)=2^(1)`

`(1+3)/(2)=2`

`(4)/(2)=2`

`2=2`

Since left hand side is equal to right side, therefore first option is correct.

Put x=2 in the given equation.

`(1)/(2)(2)+(3)/(2)=2^(2)`

`(2+3)/(2)=4`

`(5)/(2)=4`

Since left hand side is not equal to right side, therefore second option is correct.

Put x=4 in the given equation.

`(1)/(2)(4)+(3)/(2)=2^(4)`

`(4+3)/(2)=16`

`(7)/(2)=16`

Since left hand side is not equal to right side, therefore third option is correct.

Put x=8 in the given equation.

`(1)/(2)(8)+(3)/(2)=2^(8)`

`(8+3)/(2)=256`

`(11)/(2)=256`

Since left hand side is not equal to right side, therefore fourth option is correct.