Answer:
Option - 2, The solution of the equation is at x=3.
Step-by-step explanation:
Given : Equation [tex]\frac{3}{2}x+\frac{7}{2}=2^x[/tex]
To find : The point which satisfy the equation?
Solution :
To find the point we put all the given points one by one which satisfy the equation is the required point.
[tex]\frac{3}{2}x+\frac{7}{2}=2^x[/tex]
1) Put x=1,
[tex]\frac{3}{2}(1)+\frac{7}{2}=2^1[/tex]
[tex]\frac{3+7}{2}=2[/tex]
[tex]\frac{10}{2}=2[/tex]
[tex]5\neq2[/tex]
x=1 is not a point.
2) Put x=3,
[tex]\frac{3}{2}(3)+\frac{7}{2}=2^3[/tex]
[tex]\frac{9+7}{2}=8[/tex]
[tex]\frac{16}{2}=8[/tex]
[tex]8=8[/tex]
x=3 is a point satisfying equation.
3) Put x=5,
[tex]\frac{3}{2}(5)+\frac{7}{2}=2^5[/tex]
[tex]\frac{15+7}{2}=32[/tex]
[tex]\frac{22}{2}=32[/tex]
[tex]11\neq32[/tex]
x=5 is not a point.
4) Put x=8,
[tex]\frac{3}{2}(8)+\frac{7}{2}=2^8[/tex]
[tex]\frac{24+7}{2}=256[/tex]
[tex]\frac{31}{2}=256[/tex]
[tex]15.5\neq256[/tex]
x=8 is not a point.
Therefore, The solution of the equation is at x=3.
