Question

The tables below show the values of f(x) and g(x) for different values of x:

f(x) = 2(3)x


x f(x)

−2 0.22
−1 0.67
0 2
1 6
2 18


g(x) = 3x + 3

x g(x)

−2 3.11
−1 3.33
0 4
1 6
2 12


Based on the tables, what is the solution to the equation 2(3)x = 3x + 3?

x = −1

x = 0

x = 1

x = 6

Answer 1

hi,

x = 1
............

Answer 2

The correct option is 3. The solution of given equation is x=1.

Explanation:

The given functions are

`f(x)=2(3)^x`

`g(x)=3^x+3`

The table of values for both the functions are given.

The given equation is

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

The left hand side of the equation is function f(x) and right hand side of the function is g(x).

`f(x)=g(x)`

It means the solution of the given equation is the intersection point of both the functions. In other words, the solution of the function is the value of x for which the values of functions f(x) and g(x) are same.

From the given tables it is clear that the values of f(x) and g(x) are 6 at x=1.

Therefore the solution of given equation is x=1 and option 3 is correct.