Find the domain of the function 𝑓(𝑥)=log(8+3𝑥). Write your answer using interval notation.
The domain of 𝑓(𝑥) is

To find the domain of the function \( f(x) = \log(8 + 3x) \), we need to ensure that the argument of the logarithmic function is positive. Logarithms are only defined when their argument is greater than zero. Thus, we must solve the inequality:

\[
8 + 3x > 0
\]

### Step-by-step solution:
1. Subtract 8 from both sides:

\[
3x > -8
\]

2. Divide both sides by 3:

\[
x > -\frac{8}{3}
\]

Therefore, the domain of the function is all values of \( x \) greater than \( -\frac{8}{3} \).

### Answer in interval notation:
\[
\boxed{ \left( -\frac{8}{3}, \infty \right) }
\]

Would you like more details on any step or further clarification?

Here are 5 related questions you might want to explore:
1. What is the domain of \( f(x) = \log(x^2 + 1) \)?
2. How do you find the domain of a function involving square roots and logarithms?
3. What is the range of \( f(x) = \log(8 + 3x) \)?
4. Can the logarithm of a negative number ever be defined?
5. How does changing the base of the logarithm affect the domain?

**Tip:** When working with logarithmic functions, always make sure the argument of the logarithm is strictly greater than zero to determine the domain.

Find the domain of the function 𝑓(𝑥)=log(8+3𝑥). Write your answer using interval notation. The domain of 𝑓(𝑥) is

Learn how to find the domain of the logarithmic function f(x) = log(8 + 3x). This detailed step-by-step solution explains the inequalities involved and how to express the domain using interval notation. Suitable for students in Grades 10-12.

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