log 10 sqrt 2 =

Answer 1

To solve \( \log_{10} \sqrt{2} \), you can use the property of logarithms that states:

\[ \log_b(a^c) = c \cdot \log_b(a) \]

In this case, you can express \( \sqrt{2} \) as \( 2^{1/2} \):

\[ \log_{10} \sqrt{2} = \log_{10} (2^{1/2}) = \frac{1}{2} \cdot \log_{10} 2 \]

Now, you need the value of \( \log_{10} 2 \). Its approximate value is:

\[ \log_{10} 2 \approx 0.3010 \]

Now, multiply by \( \frac{1}{2} \):

\[ \log_{10} \sqrt{2} \approx \frac{1}{2} \cdot 0.3010 = 0.1505 \]

So, the value of \( \log_{10} \sqrt{2} \) is approximately \( 0.1505 \).