So I was thrilled to find the free log crochet pattern on the Club Geluk website!
The pattern is in Dutch, but I will explain some adaptation I made, and as a bonus: how to make it into a pillow.
I used 100 grams of light brown yarn (it was actually a variation yarn, but that worked well). 50 grams of beige and 50 grams of dark brown yarn. All yarn DK / light worsted (usual advice would be needle size 4). I used a crochet needle 3.5 mm to get a close firm stitch.
The recommended 43 chain stitches (light brown yarn) cast on gave me a circle of 9 1/2 cm diameter. I closed the circle and knitted 55 rows to get a 39 cm tube.
I did make a small change to the pattern in the 2 end circles of the log (beige yarn). As recommended I did cast on 8 stitches in a magic circle. And then increasing each round following in the pattern. However: I did add another round, so my outer circle was 42 stitches. This made the log end big enough for a pillow (and easy to sew on the light brown tube as the 43 and 42 stitches practically matched up one by one).
To make the inner pillow:
All measurements INCLUDING seam allowance of 1.5 cm.
Cut in a plain fabric 2 circles of 12.5 cm. And a rectangle of 35 cm x 42 cm.
Cut snippets of about 1 cm into the circles and the short sides of the rectangle (35 cm side).
The 42 cm is the length of the log. Sew along this long end to close the tube with a 1.5 cm seam.
Then pin one circle onto the tube end. Start with 2 opposite points, then on quarter points so the fabric is spread evenly throughout the circle.
Sew in round completely, again with the 1.5 cm seam. Take your time doing this. As you are sewing in a circle the rest of the fabric could pop under the needle when it shouldn't.
Repeat for second circle but leave a 5 cm gap to turn the pillow cover inside out. After the turning inside out stuff the pillow with filling. (If you always save your yarn cut-offs, that also makes a very good pillow stuffing.) Close the 5 cm gap by hand sewing.