The equation is:

$x^3 \log x = 100x$

To solve this, we can approach it step by step:

Step 1: Divide both sides by $x$

As long as $x \neq 0$, we can divide both sides of the equation by $x$:

$x^2 \log x = 100$

Step 2: Isolate $\log x$

Now, isolate $\log x$ by dividing both sides by $x^2$:

$\log x = \frac{100}{x^2}$

Step 3: Solve using numerical methods

This is a transcendental equation and doesn’t have an algebraic solution. We can solve it numerically to find the value of $x$ by plotting or using numerical approximation techniques like Newton's method.

Would you like me to calculate an approximate numerical solution for $x$?

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Here are 5 related questions for practice:

1. What is the general approach to solving transcendental equations?
2. How does the logarithmic function affect polynomial equations?
3. Can $x = 0$ ever be a solution to the equation $x^3 \log x = 100x$?
4. What are the common methods for solving non-linear equations numerically?
5. How do you apply Newton’s method to an equation like this?

Tip: For transcendental equations, graphical solutions and numerical methods are often the most effective approach!