If `6^(x) -36=7740`, then `x^(x)` =

Options

A. 7796
B. 243
C. 3125
D. 46656

Answer

To solve the equation \(6^x - 36 = 7740\), we can follow these steps:

### Step 1: Isolate \(6^x\)
We start by adding 36 to both sides of the equation to isolate \(6^x\).

\[ 6^x = 7740 + 36 \]

### Step 2: Calculate the right side
Now, we perform the addition on the right side:

\[ 6^x = 7776 \]

### Step 3: Express \(7776\) as a power of \(6\)
Next, we need to express \(7776\) as a power of \(6\). We can do this by calculating powers of \(6\):

- \(6^1 = 6\)
- \(6^2 = 36\)
- \(6^3 = 216\)
- \(6^4 = 1296\)
- \(6^5 = 7776\)

From this, we can see that:

\[ 6^x = 6^5 \]

### Step 4: Equate the exponents
Since the bases are the same, we can equate the exponents:

\[ x = 5 \]

### Step 5: Calculate \(x^x\)
Now that we have found \(x\), we need to calculate \(x^x\):

\[ x^x = 5^5 \]

### Step 6: Calculate \(5^5\)
To calculate \(5^5\):

\[ 5^5 = 5 \times 5 \times 5 \times 5 \times 5 \]

Calculating step by step:

1. \(5 \times 5 = 25\)
2. \(25 \times 5 = 125\)
3. \(125 \times 5 = 625\)
4. \(625 \times 5 = 3125\)

Thus, we find:

\[ 5^5 = 3125 \]

### Final Answer
Therefore, the value of \(x^x\) is:

\[ \boxed{3125} \]

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