Respuesta :
Answer:
First option is correct. The solution of the equation is x=1.
Step-by-step explanation:
The given equation is
[tex]\frac{1}{2}x+\frac{3}{2}=2^x[/tex]
The value of x, which satisfy the above equation is the solution of the given equation.
Put x=1 in the given equation.
[tex]\frac{1}{2}(1)+\frac{3}{2}=2^{1}[/tex]
[tex]\frac{1+3}{2}=2[/tex]
[tex]\frac{4}{2}=2[/tex]
[tex]2=2[/tex]
Since left hand side is equal to right side, therefore first option is correct.
Put x=2 in the given equation.
[tex]\frac{1}{2}(2)+\frac{3}{2}=2^{2}[/tex]
[tex]\frac{2+3}{2}=4[/tex]
[tex]\frac{5}{2}=4[/tex]
Since left hand side is not equal to right side, therefore second option is correct.
Put x=4 in the given equation.
[tex]\frac{1}{2}(4)+\frac{3}{2}=2^{4}[/tex]
[tex]\frac{4+3}{2}=16[/tex]
[tex]\frac{7}{2}=16[/tex]
Since left hand side is not equal to right side, therefore third option is correct.
Put x=8 in the given equation.
[tex]\frac{1}{2}(8)+\frac{3}{2}=2^{8}[/tex]
[tex]\frac{8+3}{2}=256[/tex]
[tex]\frac{11}{2}=256[/tex]
Since left hand side is not equal to right side, therefore fourth option is correct.
Answer:
x = 1
Step-by-step explanation:
1/2 x 1 = 1/2
1/2 + 3/2 = 4/2 = 2
2 to the power of 1 is 2
