Daily Maths Challenges

1 users here now

Share your cool maths problems.

---

---

Complete a challenge:

• Post your solution in comments, if it is exactly the same as OP's solution, let us know.
• Have fun.

---

Post a challenge:

• Doesn't have to be original, as long as it is not a duplicate.
• Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
• Optionally include solution in comments, let it be clear this is not a homework help forums.
• Tag [unsolved] if you don't have a solution yet.
• Please include images, if your question includes complex symbols, attach a render of the maths.

---

Feel free to contribute to a series by DMing the OP, or start your own challenge series.

MODERATORS

x=W(x)*e^(W(x))

x^(x*x^x)=2
x*x^x*ln(x)=ln(2)
x*e^(ln(x)*x)*ln(x)=ln(2)
u=x*ln(x)
u*e^u=ln(2)
u=W(ln(2))
x*ln(x)=W(ln(2))
e^(ln(x)*x)=e^W(ln(2))
x^x=e^W(ln(2))
x = square-super-root(e^W(ln(2)))
wikipedia says this is equivalent to:
x=e^W(ln(e^W(ln(2))))
but I don't know how they arrive at that.
x=e^W(W(ln(2))

working backwards to verify:
x=e^W(W(ln(2))
ln(x)=W(W(ln(2))
ln(x)*x=W(ln(2))
ln(x)*x*e^(ln(x)*x)=ln(2)
ln(x)*x*x^x=ln(2)
e^(ln(x)*x*x^x)=2
x^(x*x^x)=2