To solve the equation [tex]\(\log x = 4\)[/tex], follow these steps:
1. Understand Logarithmic Form:
The equation [tex]\(\log x = 4\)[/tex] indicates a common logarithm (base 10) of [tex]\(x\)[/tex] which equals 4.
2. Convert to Exponential Form:
Recall that the logarithmic equation [tex]\(\log_b a = c\)[/tex] can be rewritten in its exponential form as [tex]\(b^c = a\)[/tex]. In this case, [tex]\(b = 10\)[/tex], [tex]\(a = x\)[/tex], and [tex]\(c = 4\)[/tex].
So, the given equation [tex]\(\log x = 4\)[/tex] can be rewritten as:
[tex]\[10^4 = x\][/tex]
3. Calculate the Value:
Compute the value of [tex]\(10^4\)[/tex]:
[tex]\[10^4 = 10 \times 10 \times 10 \times 10 = 10000\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log x = 4\)[/tex] is [tex]\(10,000\)[/tex].
Hence, the answer is:
[tex]\[10,000\][/tex]
