If x is a real number and `3^x=81` , then `3xx2^x` ?

Options

A. 3
B. 16
C. 24
D. 48

Answer

To solve the equation \(3^x = 81\) and find the value of \(3 \cdot 2^x\), we can follow these steps:

### Step 1: Rewrite 81 as a power of 3
We know that \(81\) can be expressed as a power of \(3\):
\[ 81 = 3^4 \]

### Step 2: Set the exponents equal
Since the bases are the same, we can set the exponents equal to each other:
\[ x = 4 \]

### Step 3: Substitute \(x\) into the expression \(3 \cdot 2^x\)
Now that we have found \(x\), we can substitute it into the expression \(3 \cdot 2^x\):
\[ 3 \cdot 2^x = 3 \cdot 2^4 \]

### Step 4: Calculate \(2^4\)
Next, we calculate \(2^4\):
\[ 2^4 = 16 \]

### Step 5: Multiply by 3
Now we can multiply by \(3\):
\[ 3 \cdot 16 = 48 \]

### Final Answer
Thus, the value of \(3 \cdot 2^x\) is:
\[ \boxed{48} \]

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