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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

Based on the tables, what is the solution to the equation 2(3)^x = 3^x + 1? A) x= -1 B-example-1
User Liakoyras
by
7.6k points

2 Answers

7 votes

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

User HMcG
by
8.1k points
3 votes

Answer:

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.

User Artvader
by
8.3k points

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