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

Answer:

$\large\boxed{2(3)^x=3^x+3\to x=1}$

Step-by-step explanation:

Look at the picture.

Answer 2

Answer:

The solution to the equation:     $2(3)^x=3^x+3$ is:

                              x=1      

Step-by-step explanation:

The table of values for the function f(x) are as follows:

                 $f(x)=2(3)^x$

      x              f(x)

     -2             0.22

      -1              0.67

       0               2

        1               6

        2              18

The table of values for the function g(x) are as follows:

                   $g(x)=3^x+3$

        x              f(x)

      -2             3.11

      -1              3.33

       0              4

        1               6

        2              12

Now, we are asked to find the solution to the equation:

          $2(3)^x=3^x+3$

i.e. we are asked to find the x-values where both the function have the same value.

 From the table of values we observe that both the functions f(x) and g(x) have the same value at x=1.

      Hence, the answer is: x=1