For soaps critical micelle concentration (CMC) is `10^(-x)` (min) to `10^(-gamma)` (max.) mol/L what is the value of x?

Answer

To solve the problem, we need to determine the value of \( x \) given that the critical micelle concentration (CMC) of soap is expressed as \( 10^{-x} \) (minimum) to \( 10^{-y} \) (maximum) mol/L.

### Step-by-Step Solution:

1. **Understanding CMC**: The critical micelle concentration (CMC) is the concentration at which surfactants (like soap) start to form micelles. It is given in the form of \( 10^{-x} \) to \( 10^{-y} \) mol/L.

2. **Identifying Values**: From the problem statement, we know that the CMC for soap is typically in the range of \( 10^{-4} \) to \( 10^{-3} \) mol/L. This means:
- Minimum CMC = \( 10^{-4} \) mol/L
- Maximum CMC = \( 10^{-3} \) mol/L

3. **Setting the Equations**: According to the problem:
- \( 10^{-x} = 10^{-4} \) (minimum)
- \( 10^{-y} = 10^{-3} \) (maximum)

4. **Solving for \( x \)**:
- From \( 10^{-x} = 10^{-4} \), we can equate the exponents:
\[ -x = -4 \implies x = 4 \]

5. **Conclusion**: The value of \( x \) is \( 4 \).

### Final Answer:
The value of \( x \) is \( 4 \).

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