Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning.

To find the **x-intercept** of the function \( g(x) = \log(x + 4) \), we need to determine the value of \( x \) where \( g(x) = 0 \).

### Step-by-Step Process:

1. **Set \( g(x) = 0 \):**
   \[
   g(x) = \log(x + 4)
   \]
   For the x-intercept, we set \( g(x) = 0 \), so:
   \[
   \log(x + 4) = 0
   \]

2. **Use the definition of logarithm:**
   The logarithmic function \( \log_b(y) = x \) means that \( b^x = y \). In this case, we're working with the common logarithm (base 10), so we can rewrite the equation as:
   \[
   10^0 = x + 4
   \]
   Since \( 10^0 = 1 \), this simplifies to:
   \[
   1 = x + 4
   \]

3. **Solve for \( x \):**
   \[
   x = 1 - 4
   \]
   \[
   x = -3
   \]

### Conclusion:
The **x-intercept** of \( g(x) = \log(x + 4) \) is \( x = -3 \). This is the point where the graph of the function crosses the x-axis.

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Would you like a more detailed explanation of logarithms or how to work with transformations? Here are some related questions you might find interesting:

1. How does the graph of \( g(x) = \log(x + 4) \) differ from the graph of \( f(x) = \log(x) \)?
2. How would you find the x-intercept of a logarithmic function with a different base, say base 2 or base \( e \)?
3. What is the domain of the function \( g(x) = \log(x + 4) \)?
4. How would you graph the function \( g(x) = \log(x + 4) \)?
5. What is the significance of the vertical asymptote in logarithmic functions?

**Tip:** When working with logarithmic equations, remember that logarithms are only defined for positive arguments, so always ensure that the expression inside the logarithm is greater than zero.

Learn how to find the x-intercept of the logarithmic function g(x) = log(x + 4) using step-by-step reasoning. The solution involves understanding the properties of logarithms and transformations. This problem is suitable for high school students studying logarithmic functions.

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