Solve ` 2^(log_(2)(x-1))gtx+5`.

Explanation

To solve the inequality \( 2^{\log_{2}(x-1)} > x + 5 \), we will follow these steps:

### Step 1: Rewrite the left side using logarithmic properties
We can use the property of logarithms which states that \( a^{\log_{a}(b)} = b \). Here, \( a = 2 \) and \( b = x - 1 \).

\[ 2^{\log_{2}(x-1)} = x - 1 \]

### Step 2: Substitute back into the inequality
Now we can substitute this back into our inequality:

\[ x - 1 > x + 5 \]

### Step 3: Simplify the inequality
Next, we will simplify the inequality:

\[ x - 1 - x > 5 \]

This simplifies to:

\[ -1 > 5 \]

### Step 4: Analyze the result
The inequality \( -1 > 5 \) is clearly false. This indicates that there are no values of \( x \) that satisfy the original inequality.

### Conclusion
Thus, the solution to the inequality \( 2^{\log_{2}(x-1)} > x + 5 \) is that there are no valid solutions for \( x \).

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