We are given the equation:

\[
280.20 = 50 \times (1 + x)^{20}
\]

We need to solve for \( x \). Here's the step-by-step process:

### Step 1: Isolate the exponential term
Divide both sides of the equation by 50:

\[
\frac{280.20}{50} = (1 + x)^{20}
\]

This simplifies to:

\[
5.604 = (1 + x)^{20}
\]

### Step 2: Take the 20th root of both sides
To eliminate the exponent, take the 20th root of both sides:

\[
(5.604)^{\frac{1}{20}} = 1 + x
\]

Now, compute the 20th root of 5.604.

\[
5.604^{\frac{1}{20}} \approx 1.0884
\]

### Step 3: Solve for \( x \)
Now, subtract 1 from both sides:

\[
x = 1.0884 - 1
\]

\[
x \approx 0.0884
\]

Thus, \( x \approx 0.0884 \).

Would you like any further details on this solution or any specific questions? Here are some related questions to expand on this topic:

1. How do you solve for \( x \) in similar exponential equations with different powers?
2. What is the significance of taking roots in solving exponential equations?
3. Can you explain logarithms and their role in solving more complex exponential equations?
4. How do you check if an approximation of \( x \) is correct in equations like these?
5. What are some real-world applications of solving equations of this form?

**Tip:** For equations involving powers or roots, it's often helpful to rewrite the equation step by step, isolating the variable before solving.

Learn how to solve the exponential equation 280.20 = 50(1 + x)^20 with a step-by-step solution. This problem demonstrates key concepts such as exponentiation, root extraction, and isolating variables. Suitable for students in Grades 10-12.

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