Question

Based on the tables, what is the solution to the equation 2(3)^x = 3^x + 1?

A) x= -1
B) x= 0
C) x= 1
D) x=2

Answer 1

Answer: Option B.

Explanation:

The functions f(x) and g(x) are:

`f(x)=2(3)^x\\\\g(x)=3^x+1`

The equation
`2(3)^x = 3^x + 1` express that:

`f(x)=g(x)`

This means that the functions have the same output value (Value of "y") for the same input value (Value of "x").

Observe the tables and look for a common output value in the functions.

You can see that both have 2 as an output value.

The input value of
`f(x)=2` is:

`x=0`

Then:

`f(0)=2`

The output value of
`g(x)=2` is:

`x=0`

Then:

`g(0)=2`

Therefore, the solution of the equation, based on the tables, is:

`x=0`

Answer 2

x = 0

Explanation:

We are provided two expressions on both sides of the equality symbol. The solution to the equation will be the value of x which will result in the same value of both the expressions.

i.e. we have to find which value of x result in the same value of f(x) and g(x).

From the table we can see that for x = 0, both the expressions have same value i.e 2. So x = 0 is the solution to the given equation.