You can purchase hatchets from Bob's Axes in Lumbridge, he sells bronze, iron, steel and mithril hatchets.
You can also purchase axes from players on the Grand Exchange in Varrock.
For a list of all trees and requirements check out the woodcutting page.
Logs are used for training firemaking and crafting items such as arrows
Levels 1 - 10 Small Oak Tree[]
In and around Lumbridge are plenty of small trees you can cut with your bronze hatchet. They give oak logs.
They give 9 xp each, 315xp per inv.
There is a bank on top of Lumbridge Castle.
Levels 10 - 15 Palm Tree[]
On Karamja near the volcano are a swathe of palm trees you can cut with your iron hatchet. They give palm logs.
They give 10 xp each, 350 xp per inv.
It costs 30gp to travel to Karamja from Port Sarim, and 30gp to return, there is a bank deposit box in Port Sarim. (-402, 70, 702)
Alternatively you can also cut palm trees on the river side of Al Kharid.
Levels 15 - 20 Big Oak Tree[]
Behind Lumbridge castle are plenty of big oak trees that you can cut with your iron hatchet. They give oak logs.
They give 15 xp each, 525 xp per inv.
There is a bank on top of Lumbridge Castle.
Levels 20 - 30 Apple Tree[]
Head over to Edgeville, near to the Grand Exchange Agility shortcut are a few apple trees you can cut with your steel hatchet. They give oak logs,
They give 22 xp each, 770 xp per inv.
There is a bank in Edgeville, and the Grand Exchange if you have the agility level for the shortcut.
Levels 30 - 35 Willow Tree[]
At Draynor Village there are willow trees by the water that you can cut with your mithril hatchet. They give willow logs.
They give 34 xp each, 1,190 xp per inv.
There is a bank in Draynor Village.
Levels 35 - 45 Spruce Tree[]
Behind Barbarian Village and Falador farm are dark spruce trees that you can cut with your mithril hatchet. At level 40 you can use your adamant hatchet. They give spruce logs.
They give 42 xp each, 1,470 xp per inv.
There is a bank in Edgeville for Barbarian Village spruce, and Draynor Village for Falador farm spruce.
Levels 45 - 55 Maple Tree[]
Just north of Falador are maple trees that you can cut with your adamant hatchet. At level 50 you can use your rune hatchet. They give maple logs.
They give 56 xp each, 1,960 xp per inv.
There is a bank in East Falador.
Levels 55 - 60 Alpine Pine Tree[]
There are currently two version of pine tree, both pictured in this image.
West of Edgeville at the foot of the mountain are alpine pine trees that you can cut with your rune hatchet. They give pine logs.
They give 72 xp each, 2,520 per inv.
There is a bank in Edgeville.
Levels 60 - 65 Yew Tree[]
In Edgeville you can find yew trees that you can cut with your rune hatchet. They give yew logs.
Next to Cooking guild is 3 yew trees that you might prefer.
They give 87 xp each, 3,045 xp per inv.
There is a bank in Edgeville.
There is a bank in Cooking guild (lvl50 cooking needed)
Levels 65 - 75 Sequoia Tree[]
South-west of Falador near the crafting guild or west of Catherby you can find sequoia trees that you can cut with your rune hatchet. They give sequoia logs,
They give 104 xp each, 3,780 xp per inv.
There is a bank deposit box in the crafting guild if you have level 50 crafting.
There is a bank in west Falador if you have level 40 agility.
If you have neither then run baby run.
Watch out for the aggressive ents in the area, if you engage in one and run away, after about 20 seconds they will become non-hostile making it a safe area.
They can also be found west of Catherby near the bee hives.
Levels 75 - 85 Magic Tree[]
South east of the Camelot teleport heading towards Catherby are 4 magic trees. They give magic logs.
They give 136 xp each, 4,896 xp per inv.
There is a bank in Catherby.
Recommended: ignore 'Dead Willow Tree' and focus on Magic trees until Baobab.
Levels 85 - 90 Baobab Tree[]
They can be found in Taverley or plenty in north-west Karamja. They give baobab logs.
They give 190 xp each, 6,840 xp per inv.
Levels 90 - 95 Elder Tree[]
These can be found by the Black Knight Fortress, next to the Edgeville Monastery or they can be found in the Varrock park, east of Varrock. They give Elder logs.
They give 250 xp each, 9,000 xp per inv.
Levels 95 - 99 Sakura Tree[]
There are several spots to harvest Sakura trees, on Entrana via the man in the house north of Falador west bank, it costs 50gp to go there. North of Catherby, and north of Seers village also have Sakura trees. They give Sakura logs.
They give 300 xp each, 10,800 xp per inv.
There are banks at Catherby and Seers, and a bank deposit on Entrana, west of the docks.