If the third term in the expansion of `(1/x+x^(log_10x))^5` is `1000 ,` then find `x`

Explanation

To solve the problem, we need to find the value of \( x \) such that the third term in the expansion of \( \left( \frac{1}{x} + x^{\log_{10} x} \right)^5 \) is equal to 1000.

### Step-by-Step Solution:

1. **Identify the Binomial Expansion**:
The expression can be written as \( (a + b)^n \) where \( a = \frac{1}{x} \), \( b = x^{\log_{10} x} \), and \( n = 5 \).

2. **Find the Third Term**:
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