The `log_100x=-4,` then the value of x is :

Options

A. `1/(10)^(-4)`
B. `(10)^(-4)`
C. `1/(10)^8`
D. none of these

Answer

To solve the equation \( \log_{100} x = -4 \), we can follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
Using the property of logarithms, we can rewrite the equation \( \log_{a} b = c \) as \( b = a^{c} \). In our case, this means:
\[ 100^{{-4}} = x \]

### Step 2: Simplify \( 100^{-4} \)
Next, we can express \( 100 \) as \( 10^2 \):
\[ x = (10^2)^{-4} \]
Using the power of a power property \( (a^m)^n = a^{m \cdot n} \), we get:
\[ x = 10^{2 \cdot (-4)} = 10^{-8} \]

### Step 3: Express \( 10^{-8} \) in a different form
We can rewrite \( 10^{-8} \) as:
\[ x = \frac{1}{10^8} \]

### Conclusion
Thus, the value of \( x \) is:
\[ x = \frac{1}{10^8} \]

### Final Answer
The value of \( x \) is \( \frac{1}{10^8} \).

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