This math puzzle is blowing up online — and it looks deceptively easy. Is x = 7? Let’s test it: 7^7 = 823,543. Not even close.
Here’s what actually happens when you try the integers:
- 2^2 = 4
- 3^3 = 27
- 4^4 = 256
49 sits between 3^3 = 27 and 4^4 = 256, so x is somewhere between 3 and 4. But there’s no clean integer answer — so how do we find it?
Step 1: Take the log of both sides
x^x = 49 becomes:
x · ln(x) = ln(49) ≈ 3.892
Step 2: Solve for x
Rewrite the left side as ln(x) · e^{ln(x)} = ln(49). This matches the form u · e^u = c, which is solved by the Lambert W function:
ln(x) = W(ln 49), so x = e^{W(ln 49)} ≈ 3.278
Step 3: Check the answer
3.278^3.278 = e^{3.278 · ln(3.278)} = e^{3.892} ≈ 49 ✓
Answer: x ≈ 3.278
Why this puzzle works so well
Most people guess 7 — because 7 × 7 = 49. The trap is confusing x × x with x^x. Self-power equations (tetration-style, x raised to itself) grow insanely fast, so the answer is always much smaller than your gut says.
Want more of these? Try x^x = 27 (hint: exactly 3) or x^x = 256 (exactly 4).