To solve the equation [tex]\(\log(2x) = 2\)[/tex], follow these steps:
1. Understand that [tex]\(\log\)[/tex] without a base explicitly given typically refers to [tex]\(\log_{10}\)[/tex], the common logarithm. So we rephrase the given equation as:
[tex]\[
\log_{10}(2x) = 2
\][/tex]
2. Rewrite the logarithmic equation in its exponential form. Recall that [tex]\(a = \log_{b}(c)\)[/tex] can be rewritten as [tex]\(b^a = c\)[/tex]. Applying this principle here:
[tex]\[
10^2 = 2x
\][/tex]
3. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
4. Solve for [tex]\(x\)[/tex] by isolating it on one side of the equation:
[tex]\[
2x = 100
\][/tex]
[tex]\[
x = \frac{100}{2}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 50
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log(2x) = 2\)[/tex] is [tex]\(\boxed{50}\)[/tex].
