To find the domain of the function [tex]\( y = \log(1 - 2x) \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which the argument of the logarithm is positive, as the logarithmic function is only defined for positive arguments.
1. Start by identifying the condition for the argument of the logarithm to be positive:
[tex]\[
1 - 2x > 0
\][/tex]
2. Solve the inequality:
[tex]\[
1 - 2x > 0
\][/tex]
Subtract 1 from both sides:
[tex]\[
-2x > -1
\][/tex]
Divide both sides by -2. Remember that dividing by a negative number reverses the inequality:
[tex]\[
x < \frac{1}{2}
\][/tex]
3. This inequality tells us that [tex]\( x \)[/tex] must be less than [tex]\( \frac{1}{2} \)[/tex].
So, the domain of the function [tex]\( y = \log(1 - 2x) \)[/tex] in interval notation is:
[tex]\[
(-\infty, \frac{1}{2})
\][/tex]
Thus, the domain is:
[tex]\[
\boxed{(-\infty, \frac{1}{2})}
\][/tex]
