If `3^(x-1)+5^(x-1)=34`, then x= …..

Answer

To solve the equation \( 3^{(x-1)} + 5^{(x-1)} = 34 \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ 3^{(x-1)} + 5^{(x-1)} = 34 \]

### Step 2: Substitute variables
Let \( k = x - 1 \). Then, we can rewrite the equation as:
\[ 3^k + 5^k = 34 \]

### Step 3: Test integer values for \( k \)
We will test integer values for \( k \) to find a solution.

- For \( k = 2 \):
\[ 3^2 + 5^2 = 9 + 25 = 34 \]
This satisfies the equation.

### Step 4: Find \( x \)
Since we found \( k = 2 \):
\[ k = x - 1 \implies 2 = x - 1 \implies x = 3 \]

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

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