If `log_(100)x =-1/2`, then the value of x is:

Options

A. 0.001
B. `1/10`
C. 1.0E-5
D. `10^(-2)`

Answer

To solve the equation \( \log_{100} x = -\frac{1}{2} \), we can follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
The logarithmic equation \( \log_{b} a = c \) can be rewritten in exponential form as \( a = b^c \).

In this case, we have:
\[ x = 100^{-\frac{1}{2}} \]

### Step 2: Simplify the expression
Next, we simplify \( 100^{-\frac{1}{2}} \). The negative exponent indicates that we take the reciprocal:
\[ 100^{-\frac{1}{2}} = \frac{1}{100^{\frac{1}{2}}} \]

### Step 3: Calculate \( 100^{\frac{1}{2}} \)
The expression \( 100^{\frac{1}{2}} \) represents the square root of 100:
\[ 100^{\frac{1}{2}} = \sqrt{100} = 10 \]

### Step 4: Substitute back to find \( x \)
Now we substitute back into our expression for \( x \):
\[ x = \frac{1}{10} \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{\frac{1}{10}} \]

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