Write the domain of the following real functions
`log(2-3x)`

Answer

To find the domain of the function \( f(x) = \log(2 - 3x) \), we need to ensure that the argument of the logarithm is positive. The logarithm function is defined only for positive values.

### Step-by-Step Solution:

1. **Identify the argument of the logarithm**: The function is \( f(x) = \log(2 - 3x) \). Here, the argument is \( 2 - 3x \).

2. **Set the argument greater than zero**: For the logarithm to be defined, we need:
\[ 2 - 3x > 0 \]

3. **Solve the inequality**:
- Rearranging the inequality gives:
\[ -3x > -2 \]
- Dividing both sides by -3 (remember to reverse the inequality sign when dividing by a negative number):
\[ x < \frac{2}{3} \]

4. **Express the domain in interval notation**: The solution \( x < \frac{2}{3} \) means that \( x \) can take any value less than \( \frac{2}{3} \). Therefore, the domain of the function in interval notation is:
\[ (-\infty, \frac{2}{3}) \]

### Final Answer:
The domain of the function \( f(x) = \log(2 - 3x) \) is:
\[ (-\infty, \frac{2}{3}) \]