Answer:
(B) x=3
Step-by-step explanation:
The given equation can be written as:
[tex]\frac{3}{2}x+\frac{7}{2}=2^x[/tex]
(A) Substituting the value of x=1. we get
[tex]\frac{3}{2}+\frac{7}{2}=2[/tex]
[tex]5=2[/tex]
which is not possible, therefore x=1 is not the solution of the given equation.
(B) Substituting the value of x=3, we get
[tex]\frac{3}{2}(3)+\frac{7}{2}=2^3[/tex]
[tex]\frac{9}{2}+\frac{7}{2}=8[/tex]
[tex]8=8[/tex]
which is possible, therefore x=3 is the solution of the given equation.
(C) Substiuting the value of x=5, we get
[tex]\frac{3}{2}(5)+\frac{7}{2}=2^5[/tex]
[tex]\frac{15}{2}+\frac{7}{2}=32[/tex]
[tex]11=32[/tex]
which is not possible, therefore x=5 is not the solution of the given equation.
(D) Substituting the value of x-8, we get
[tex]\frac{3}{2}(8)+\frac{7}{2}=2^8[/tex]
[tex]\frac{31}{2}=256[/tex]
which is not possible, therefore x=8 is not the solution of the given equation.
