To solve the equation [tex]\(\log x = 3\)[/tex], we need to find the value of [tex]\(x\)[/tex] that satisfies this equation. Let’s break down the steps:
1. Understanding Logarithms: The expression [tex]\(\log x\)[/tex] generally refers to the common logarithm, which is the logarithm base 10 (i.e., [tex]\(\log_{10} x\)[/tex]). So, the equation [tex]\(\log_{10} x = 3\)[/tex] can be interpreted as:
[tex]\[
10^{\log_{10} x} = 10^3
\][/tex]
2. Eliminating the Logarithm: Using the property of logarithms that states [tex]\(10^{\log_{10} x} = x\)[/tex], we can rewrite the equation as:
[tex]\[
x = 10^3
\][/tex]
3. Calculating the Value: Now, we need to compute the power of 10:
[tex]\[
10^3 = 10 \times 10 \times 10 = 1000
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log x = 3\)[/tex] is [tex]\(1000\)[/tex].
Among the given multiple-choice options, the correct answer is:
[tex]\[ \boxed{1,000} \][/tex]
