To find the value of [tex]\(\log_{10} 4 + \log_{10} 25\)[/tex], we can use the properties of logarithms. Here are the steps in detail:
1. Evaluate [tex]\(\log_{10} 4\)[/tex]:
By calculating, we find:
[tex]\[
\log_{10} 4 \approx 0.6020599913279624
\][/tex]
2. Evaluate [tex]\(\log_{10} 25\)[/tex]:
Similarly, we get:
[tex]\[
\log_{10} 25 \approx 1.3979400086720377
\][/tex]
3. Add the two logarithmic values:
Adding these values together:
[tex]\[
\log_{10} 4 + \log_{10} 25 \approx 0.6020599913279624 + 1.3979400086720377 = 2.0
\][/tex]
4. Verify the addition using logarithmic properties:
We can use the property of logarithms which states:
[tex]\[
\log_{10} a + \log_{10} b = \log_{10} (a \times b)
\][/tex]
Therefore:
[tex]\[
\log_{10} 4 + \log_{10} 25 = \log_{10} (4 \times 25)
\][/tex]
5. Calculate the product inside the logarithm:
[tex]\[
4 \times 25 = 100
\][/tex]
6. Evaluate [tex]\(\log_{10} 100\)[/tex]:
[tex]\[
\log_{10} 100 = 2
\][/tex]
Putting it all together, we find that:
[tex]\[
\log_{10} 4 + \log_{10} 25 = \log_{10} 100 = 2
\][/tex]
So, the final value is:
[tex]\[
2.0
\][/tex]
Thus, [tex]\(\log_{10} 4 + \log_{10} 25 = 2.0\)[/tex].
