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

x	-2	-1	0	1	2
f(x)	0.22	0.67	2	6	18

g(x) = 3^x + 1

x	-2	-1	0	1	2
f(x)	1.11	1.33	2	4	10

Solution:

Given, the equation 2(3)^x = 3^x + 1

We have to find the solution to the equation based on the given table.

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

Let g(x) = 3^x + 1

So, f(x) = g(x)

This means that the functions have the same output value for the same input value.

From the table, we observe for the common output value in the functions.

Both f(x) and g(x) 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 table is x = 0.

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

Summary:

Based on the tables, the solution to the equation 2(3)^x = 3^x + 1 is x = 0.