If `2xx2^(x)=16`, what is x?

Answer

To solve the equation \( 2 \times 2^x = 16 \), we can follow these steps:

### Step 1: Rewrite the left-hand side using the laws of exponents
We know that when multiplying powers with the same base, we can add the exponents. Thus, we can rewrite \( 2 \times 2^x \) as:
\[ 2^1 \times 2^x = 2^{1+x} \]
So, we have:
\[ 2^{1+x} = 16 \]

### Step 2: Express 16 as a power of 2
Next, we need to express 16 as a power of 2. We know that:
\[ 16 = 2^4 \]
Now we can rewrite our equation:
\[ 2^{1+x} = 2^4 \]

### Step 3: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:
\[ 1 + x = 4 \]

### Step 4: Solve for x
Now, we can solve for \( x \) by isolating it:
\[ x = 4 - 1 \]
\[ x = 3 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{3} \]

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