If `10^((log_10|x|)`=2, what is the value of x ?

Options

A. 2 only
B. `-2` only
C. 2 or `-2`
D. 1 or `-1`

Explanation

To solve the equation \( 10^{(\log_{10}|x|)} = 2 \), we will follow these steps:

### Step 1: Apply logarithm to both sides
Take the logarithm base 10 of both sides of the equation:
\[ \log_{10}(10^{(\log_{10}|x|)}) = \log_{10}(2) \]

### Step 2: Simplify the left side
Using the property of logarithms that states \( \log_{10}(10^a) = a \), we can simplify the left side:
\[ \log_{10}|x| = \log_{10}(2) \]

### Step 3: Remove the logarithm
To remove the logarithm, we can exponentiate both sides with base 10:
\[ |x| = 2 \]

### Step 4: Solve for x
The absolute value equation \( |x| = 2 \) gives us two possible solutions:
\[ x = 2 \quad \text{or} \quad x = -2 \]

### Final Answer
Thus, the values of \( x \) are:
\[ x = 2 \quad \text{or} \quad x = -2 \]

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