The expression you've provided is:

\[
4 \log(x) + 13x
\]

This is a combination of two terms: one involving a logarithmic function and the other a linear term. If you're looking for something specific, like solving, simplifying, or differentiating this expression, here are some possibilities:

### 1. Simplifying:
The expression is already in its simplest form.

### 2. Solving for \( x \):
If you were looking for a solution to an equation (e.g., \( 4 \log(x) + 13x = 0 \)), we'd need to set it equal to some value, typically 0, and solve for \( x \).

### 3. Differentiation:
If we differentiate this expression with respect to \( x \), we can apply the derivative rules:
- The derivative of \( \log(x) \) is \( \frac{1}{x} \).
- The derivative of \( 13x \) is 13.

So, the derivative \( \frac{d}{dx} \) of the expression is:

\[
\frac{d}{dx}\left(4 \log(x) + 13x\right) = 4 \cdot \frac{1}{x} + 13 = \frac{4}{x} + 13
\]

### 4. Graphing:
If you wanted to visualize the behavior of this function, I can help plot it for you.

Let me know which approach you'd like to take!

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Do you want to explore more details, or have any specific questions? Here are some related problems:

1. Solve the equation \( 4 \log(x) + 13x = 0 \) for \( x \).
2. Differentiate \( 3 \log(x) + 5x^2 \).
3. Find the integral of \( 4 \log(x) + 13x \).
4. What is the domain of \( f(x) = 4 \log(x) + 13x \)?
5. Solve \( \log(x) + x = 3 \) for \( x \).

**Tip**: When solving logarithmic equations, always check that the solution is in the domain of the logarithmic function (i.e., \( x > 0 \)).

Explore how to differentiate and solve the logarithmic expression 4log(x) + 13x. Learn about key mathematical concepts such as logarithms, linear functions, and differentiation with detailed steps for high school students in Grades 10-12.

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