Solve the following expressions .
`3^(x - 1) + 3^(x + 1) = 90` then x = ?

Answer

To solve the equation \( 3^{(x - 1)} + 3^{(x + 1)} = 90 \), we can follow these steps:

### Step 1: Rewrite the terms
We start with the equation:
\[ 3^{(x - 1)} + 3^{(x + 1)} = 90 \]
We can rewrite \( 3^{(x + 1)} \) as \( 3^{(x - 1 + 2)} = 3^{(x - 1)} \cdot 3^2 = 9 \cdot 3^{(x - 1)} \). Thus, we can rewrite the equation as:
\[ 3^{(x - 1)} + 9 \cdot 3^{(x - 1)} = 90 \]

### Step 2: Combine like terms
Now, we can factor out \( 3^{(x - 1)} \):
\[ 3^{(x - 1)} (1 + 9) = 90 \]
This simplifies to:
\[ 10 \cdot 3^{(x - 1)} = 90 \]

### Step 3: Isolate \( 3^{(x - 1)} \)
Next, we divide both sides by 10:
\[ 3^{(x - 1)} = \frac{90}{10} = 9 \]

### Step 4: Rewrite 9 as a power of 3
We know that \( 9 = 3^2 \), so we can rewrite the equation as:
\[ 3^{(x - 1)} = 3^2 \]

### Step 5: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 1 = 2 \]

### Step 6: Solve for \( x \)
Now, we solve for \( x \):
\[ x = 2 + 1 = 3 \]

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