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.

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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.