If `log_(10)m=(1)/(2)`, then `log_(10)10m^(2)=`

Options

A. 2
B. 2.5
C. 3
D. 10.25

Explanation

To solve the problem, we need to find the value of \( \log_{10}(10m^2) \) given that \( \log_{10} m = \frac{1}{2} \).

### Step-by-step Solution:

1. **Start with the given information:**
\[ \log_{10} m = \frac{1}{2} \]

2. **Use the property of logarithms for multiplication:**
The logarithm of a product can be expressed as the sum of the logarithms:
\[ \log_{10}(10m^2) = \log_{10}(10) + \log_{10}(m^2) \]

3. **Calculate \( \log_{10}(10) \):**
We know that:
\[ \log_{10}(10) = 1 \]

4. **Use the property of logarithms for exponents:**
The logarithm of a power can be expressed as the exponent times the logarithm of the base:
\[ \log_{10}(m^2) = 2 \log_{10}(m) \]

5. **Substitute the value of \( \log_{10}(m) \):**
From the given information, we have:
\[ \log_{10}(m) = \frac{1}{2} \]
Therefore:
\[ \log_{10}(m^2) = 2 \cdot \frac{1}{2} = 1 \]

6. **Combine the results:**
Now substitute back into the equation:
\[ \log_{10}(10m^2) = \log_{10}(10) + \log_{10}(m^2) = 1 + 1 = 2 \]

### Final Answer:
\[ \log_{10}(10m^2) = 2 \]