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

This problem solves the equation 2^(x+1) - 3^x = 0 for x using logarithmic properties. The solution is x = 1 / (log₂(3) - 1), which is approximately 2.7095.

Answer

Let’s solve this equation step by step:

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:

Therefore, the solution is:

This can be approximated to about 2.7095 if a decimal answer is needed.

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

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