I suppose you just get a new image where the image is the log of the pixel value. It's used to enhance dark areas by expanding their range, while not clipping bright areas. Run the code below for a demo.
workspace;
grayImage = imread('Cameraman.tif');
grayImage = double(grayImage);
subplot(2,1,1);
imshow(grayImage, []);
axis on;
title('Original Image', 'FontSize', 15);
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
logImage = log(grayImage+1);
normalizedImage = mat2gray(logImage);
subplot(2,1,2);
imshow(normalizedImage, []);
axis on;
title('Log Image', 'FontSize', 15);
msgbox('Note how the coat has more details');
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