The value of `log_(10)(0.0001)` is:

Options

A. `1/1000`
B. `-3`
C. `-4`
D. none of these

Answer

To find the value of \( \log_{10}(0.0001) \), we can follow these steps:

### Step 1: Rewrite the number in scientific notation
The number \( 0.0001 \) can be rewritten in scientific notation.
\[ 0.0001 = 1 \times 10^{-4} \]

### Step 2: Apply the logarithmic property
Using the property of logarithms that states \( \log_{a}(b \times c) = \log_{a}(b) + \log_{a}(c) \), we can express the logarithm of a product:
\[ \log_{10}(0.0001) = \log_{10}(1 \times 10^{-4}) = \log_{10}(1) + \log_{10}(10^{-4}) \]

### Step 3: Calculate each logarithm
We know that \( \log_{10}(1) = 0 \) because any number to the power of 0 is 1. Now we calculate \( \log_{10}(10^{-4}) \):
\[ \log_{10}(10^{-4}) = -4 \]

### Step 4: Combine the results
Now, we can combine the results from Step 2:
\[ \log_{10}(0.0001) = 0 + (-4) = -4 \]

### Final Answer
Thus, the value of \( \log_{10}(0.0001) \) is:
\[ \boxed{-4} \]

---