Question

PLZ HELP!!!

An equation is shown below: 3 over 2 multiplied by x plus 7 over 2 equals 2 to the power of x What is the solution to the equation?
A. x = 1
B. x = 3
C. x = 5
D. x = 8

Answer 1

(B) x=3

Explanation:

The given equation can be written as:

`(3)/(2)x+(7)/(2)=2^x`

(A) Substituting the value of x=1. we get

`(3)/(2)+(7)/(2)=2`

`5=2`

which is not possible, therefore x=1 is not the solution of the given equation.

(B) Substituting the value of x=3, we get

`(3)/(2)(3)+(7)/(2)=2^3`

`(9)/(2)+(7)/(2)=8`

`8=8`

which is possible, therefore x=3 is the solution of the given equation.

(C) Substiuting the value of x=5, we get

`(3)/(2)(5)+(7)/(2)=2^5`

`(15)/(2)+(7)/(2)=32`

`11=32`

which is not possible, therefore x=5 is not the solution of the given equation.

(D) Substituting the value of x-8, we get

`(3)/(2)(8)+(7)/(2)=2^8`

`(31)/(2)=256`

which is not possible, therefore x=8 is not the solution of the given equation.