The value of `log_(10)(0.000010)` is

Options

A. (-5)
B. (-6)
C. (-7)
D. none of these

Answer

To find the value of \( \log_{10}(0.000010) \), we can follow these steps:

### Step 1: Rewrite the number in scientific notation
We can express \( 0.000010 \) in scientific notation:
\[ 0.000010 = 1 \times 10^{-5} \]

### Step 2: Apply the logarithmic property
Using the logarithmic property \( \log_{b}(mn) = \log_{b}(m) + \log_{b}(n) \), we can rewrite our expression:
\[ \log_{10}(0.000010) = \log_{10}(1 \times 10^{-5}) = \log_{10}(1) + \log_{10}(10^{-5}) \]

### Step 3: Calculate \( \log_{10}(1) \)
We know that:
\[ \log_{10}(1) = 0 \]

### Step 4: Calculate \( \log_{10}(10^{-5}) \)
Using the property \( \log_{b}(b^n) = n \):
\[ \log_{10}(10^{-5}) = -5 \]

### Step 5: Combine the results
Now we can combine the results from Step 3 and Step 4:
\[ \log_{10}(0.000010) = 0 + (-5) = -5 \]

### Final Answer
Thus, the value of \( \log_{10}(0.000010) \) is:
\[ \boxed{-5} \]

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