Solve for x in the following equations.
`7^(x-2)=49`

Answer

To solve the equation \( 7^{(x-2)} = 49 \), we can follow these steps:

### Step 1: Rewrite 49 as a power of 7
We know that \( 49 \) can be expressed as \( 7^2 \). Therefore, we can rewrite the equation:
\[ 7^{(x-2)} = 7^2 \]

**Hint for Step 1:** Look for a way to express the number on the right side of the equation as a power of the same base as the left side.

### Step 2: Set the exponents equal to each other
Since the bases are the same (both are base 7), we can set the exponents equal to each other:
\[ x - 2 = 2 \]

**Hint for Step 2:** When the bases are the same, you can equate the exponents directly.

### Step 3: Solve for x
Now, we can solve for \( x \) by adding 2 to both sides of the equation:
\[ x = 2 + 2 \]
\[ x = 4 \]

**Hint for Step 3:** Isolate \( x \) by performing inverse operations on both sides of the equation.

### Final Answer
The solution to the equation \( 7^{(x-2)} = 49 \) is:
\[ \boxed{4} \]