To solve the expression [tex]\(2 - 2 \log 5\)[/tex], we will break it down step by step.
1. Understand the logarithm: We know the logarithm is the inverse of exponentiation. Here, [tex]\(\log\)[/tex] without a base specified usually refers to the common logarithm with a base 10, i.e., [tex]\(\log_{10}\)[/tex].
2. Calculate the logarithm of 5: The value of [tex]\(\log_{10} 5\)[/tex] is a fixed numerical value which represents the power to which the base 10 must be raised to produce the number 5. Based on precomputed logarithm tables or a scientific calculator:
[tex]\[
\log_{10} 5 \approx 0.69897
\][/tex]
3. Multiply by 2: Next, we multiply the logarithm by 2:
[tex]\[
2 \times \log_{10} 5 \approx 2 \times 0.69897 = 1.39794
\][/tex]
4. Subtract the product from 2: Finally, we subtract this result from 2:
[tex]\[
2 - 1.39794 = 0.60206
\][/tex]
Therefore, the result of the expression [tex]\(2 - 2 \log 5\)[/tex] is approximately [tex]\(0.60206\)[/tex].
