The equation you've provided is:

\[
x \cdot \log_{10}(x) = 100x
\]

Let's solve this equation step by step.

### Step 1: Simplify the equation
We can start by dividing both sides of the equation by \(x\) (assuming \(x \neq 0\)):

\[
\log_{10}(x) = 100
\]

### Step 2: Solve for \(x\)
The logarithm equation can be rewritten in exponential form:

\[
x = 10^{100}
\]

### Step 3: Interpret the result
The solution to the equation is:

\[
x = 10^{100}
\]

This is an extremely large number, often referred to as a **googol** in mathematical terms.

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the value of \( \log_{10}(10^{100}) \)?
2. How does the solution change if the equation were \( x \cdot \log_{10}(x) = 10x \)?
3. Can you solve \( x \cdot \log_{10}(x) = 100 \) for \(x\)?
4. What happens if the logarithm is in a different base, such as \( \log_{2}(x) \)?
5. How would you graph the function \( y = x \cdot \log_{10}(x) \) compared to \( y = 100x \)?

### Tip:
When dealing with logarithmic equations, converting to the exponential form is often the key step to solving for the variable.

Learn how to solve the equation x log10 power x = 100x step-by-step with a detailed explanation. This problem involves logarithms and exponential equations, suitable for advanced high school students and anyone interested in mathematical problem-solving.

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