# What is the solution to the equation 2(3)^{x} = 3^{x} + 1?

**Solution:**

Given, the equation is 2(3)^{x} = 3^{x} + 1.

We have to find the solution of the equation.

The given equation can be written as

2(3)^{x} - 3^{x} = 1

By grouping,

3^{x}(2 - 1 ) = 1

3^{x} = 1

By applying logarithmic property,

\(loga^{b}=blog_{a}\)

So, ln(3^{x}) = ln(1)

xln(3) = ln(1)

x = ln(1)/ln(3)

We know, ln(3) =0.477

ln(1) = 0

So, x =0.477/0

x = 0

Therefore, the solution of the equation is x = 0.

## What is the solution to the equation 2(3)^{x} = 3^{x} + 1?

**Summary:**

The solution to the equation 2(3)^{x} = 3^{x} + 1 is 0.

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