Solve for x: 2^(x+1) - 3^x = 0

We start with the equation:

To solve this, we can move all terms to one side:

Now, let’s use the properties of exponents to simplify the left side:

We can divide both sides by :

Now, we can take the logarithm of both sides. Let’s use log base 2:

The left side simplifies to 1, and we can use the logarithm property on the right:

Now we can solve for x:

We can simplify this further: