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## Homework Statement

Solve for x

(1/10)^(x - 1) < (1/10)

**2. My Dilemma**

The problem is that using one method will yield one answer, but using another method will yield another. Why is that? Please help.

My issue is not regarding the right answer (the right answer is x > 2). It's regarding the method/mathematical operation. Thanks!

**3. Solution attempts**

Method 1: Multiplying exponents (this method should be the correct one)

Step 1: (10^-1)^(x - 1) < 10^-1

Step 2: multiply exponents:: 10^(-x + 1) < 10^-1

Step 3: simplify:: -x + 1 < -1

Step 4: solve:: x > 2

Method 2: Please tell me what's wrong with this method

Step 1: [(1/10)^x] / (1/10) < (1/10)

Step 2: multiply both sides by (1/10):: (1/10)^x < (1/10)^2

Step 3: solve:: x < 2