To solve the equation [tex]\(\log(2x) = 2\)[/tex], we need to follow these steps:
1. Recognize that [tex]\(\log(2x) = 2\)[/tex] is in base 10 (common logarithm).
2. Convert the logarithmic equation to its exponential form. The equation [tex]\(\log_{10}(2x) = 2\)[/tex] can be rewritten as:
[tex]\[
2x = 10^2
\][/tex]
3. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
4. Now, we have:
[tex]\[
2x = 100
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 2:
[tex]\[
x = \frac{100}{2}
\][/tex]
6. Simplify the division:
[tex]\[
x = 50
\][/tex]
The value of [tex]\(x\)[/tex] is [tex]\(50\)[/tex].
