Solve for x : `5^(x)root(x)(8^(x-1))=500`

Explanation

To solve the equation \( 5^x \cdot \sqrt[x]{8^{x-1}} = 500 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 5^x \cdot \sqrt[x]{8^{x-1}} = 500 \]
We can rewrite the term \( \sqrt[x]{8^{x-1}} \) as \( (8^{x-1})^{\frac{1}{x}} \). This gives us:
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