\( \operatorname { Ln } ( x ^ { 3 } ( 2 x - 5 ) ! ) \)

To simplify the expression \( \operatorname{Ln}(x^3 (2x - 5)!) \), we can use the properties of logarithms. 1. **Apply the logarithm property**: The logarithm of a product can be expressed as the sum of the logarithms: \[ \operatorname{Ln}(a \cdot b) = \operatorname{Ln}(a) + \operatorname{Ln}(b) \] Therefore, we can rewrite the expression as: \[ \operatorname{Ln}(x^3) + \operatorname{Ln}((2x - 5)!) \] 2. **Simplify \( \operatorname{Ln}(x^3) \)**: Using the power rule of logarithms: \[ \operatorname{Ln}(x^3) = 3 \cdot \operatorname{Ln}(x) \] 3. **Combine the results**: The expression now becomes: \[ 3 \cdot \operatorname{Ln}(x) + \operatorname{Ln}((2x - 5)!) \] Thus, the simplified form of the expression \( \operatorname{Ln}(x^3 (2x - 5)!) \) is: \[ 3 \cdot \operatorname{Ln}(x) + \operatorname{Ln}((2x - 5)!) \]