Answer :
To solve the logarithmic equation [tex]\(\log x = 4\)[/tex], we need to convert it to its equivalent exponential form.
The logarithmic equation [tex]\(\log x = 4\)[/tex] is in base 10, which is implicit when the base is not specified. Therefore, we can rewrite it explicitly as [tex]\(\log_{10} x = 4\)[/tex].
To convert this logarithmic equation to an exponential equation, we use the definition of logarithms:
[tex]\[ \log_{b}(x) = y \implies b^y = x \][/tex]
In this case, [tex]\(b = 10\)[/tex], [tex]\(y = 4\)[/tex], and [tex]\(x = x\)[/tex]. Applying the definition:
[tex]\[ \log_{10}(x) = 4 \implies 10^4 = x \][/tex]
So the exponential form of the given logarithmic equation is:
[tex]\[ 10^4 = x \][/tex]
Thus, the correct exponential equation corresponding to [tex]\(\log x = 4\)[/tex] is:
B. [tex]\(10^4 = x\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
The logarithmic equation [tex]\(\log x = 4\)[/tex] is in base 10, which is implicit when the base is not specified. Therefore, we can rewrite it explicitly as [tex]\(\log_{10} x = 4\)[/tex].
To convert this logarithmic equation to an exponential equation, we use the definition of logarithms:
[tex]\[ \log_{b}(x) = y \implies b^y = x \][/tex]
In this case, [tex]\(b = 10\)[/tex], [tex]\(y = 4\)[/tex], and [tex]\(x = x\)[/tex]. Applying the definition:
[tex]\[ \log_{10}(x) = 4 \implies 10^4 = x \][/tex]
So the exponential form of the given logarithmic equation is:
[tex]\[ 10^4 = x \][/tex]
Thus, the correct exponential equation corresponding to [tex]\(\log x = 4\)[/tex] is:
B. [tex]\(10^4 = x\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
