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

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

Explanation:

Look at the picture.

Answer 2

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

x=1

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