Solve for x:
` log_(sqrt3) (x+1) = 2 `

Answer

To solve the equation \( \log_{\sqrt{3}} (x + 1) = 2 \), we can follow these steps:

### Step 1: Use the definition of logarithms
The equation \( \log_{\sqrt{3}} (x + 1) = 2 \) can be rewritten using the definition of logarithms. According to the property of logarithms, if \( \log_b(a) = c \), then \( a = b^c \).

So, we can rewrite our equation as:
\[ x + 1 = (\sqrt{3})^2 \]

### Step 2: Simplify the right side
Now, we need to simplify \( (\sqrt{3})^2 \):
\[ (\sqrt{3})^2 = 3 \]

### Step 3: Set up the equation
Now we have:
\[ x + 1 = 3 \]

### Step 4: Solve for \( x \)
To find \( x \), we subtract 1 from both sides:
\[ x = 3 - 1 \]
\[ x = 2 \]

### Final Answer
Thus, the solution for \( x \) is:
\[ \boxed{2} \]

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