Define the following intensity transformation functions, with suitable examples: 
 i) Log Transformations
 ii) Power-Law (Gamma) Transformations. 

Intensity transformations play a crucial role in image processing, aiding in the enhancement and manipulation of image characteristics. Two common transformations are log transformations and power-law (gamma) transformations.

i) Log Transformations:
Log transformations are employed to expand the dynamic range of images, particularly useful when images exhibit low contrast. The transformation is expressed as \( s = c \cdot \log(1 + r) \), ____ ____ ________ ________ ________ ____ _______ _______ _______ _______.
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