The video presents a challenging SAT-style math problem: finding a number 'x' such that x raised to the power of itself equals 25 (x^x = 25). The presenter initially considers simple integer solutions, demonstrating that 5^5 is 3125, which is too large, and 2^2 is 4, which is too small. They also test 3^3, which is 27, also too large. This leads to the conclusion that the solution for 'x' must lie between 2 and 3. The presenter then introduces the concept of using the natural logarithm (ln) as a mathematical tool to solve this type of equation. By taking the natural log of both sides of the equation x^x = 25, they transform it into x * ln(x) = ln(25). However, they acknowledge that even with this transformation, solving for 'x' directly is difficult and requires another advanced mathematical tool: the Lambert W function. The video concludes by stating the approximate numerical solution for x is 2.947, obtained using this function, and encourages viewers to watch another video for more SAT hacks.

Your SAT Coach

Can you solve this trick SAT question? We're looking for some mystery number x that raised to the power of itself is 25.

Well, easy. 5. 5 to the 5th. Oh, 3,125. Well, I meant 5 squared. That's 20. But it's x to the x. The two numbers need to be the same.

Oh. Oh, so 2, dude. Slow down. 2 ^ 2 is 4. Way too small. And 3 cubed. 3 * 3 * 3 is 27. Too big. Okay, but the answer has to be somewhere between 2 and 3. That's at least a rule we've proved now.

But the problem is we can't solve this like this. X is mad stuck. So, we need to use a secret little math weapon. The natural log. Natural log is badass. It helps us pull the exponent down into something we can handle.

So, if we take the natural log of both sides, the natural log of x to the x [music] brings the exponent down and out front. So we get x ln x is equal to ln25.

Now I would still probably guess and check values between 2 and three on this but technically you need to use another secret weapon to solve this. The lambert w function and that yanni lets you go uh boop boop boop and uh boop boop boop x is like 2.947.

Want more SAT hacks? Click the video below.

Tricky SAT question..

Can you solve this trick SAT question?
We're looking for some mystery number x
that raised to the power of itself is
25. Well, easy. 5. 5 to the 5th. Oh,
3,125.
Well, I meant 5 squared. That's 20. But
it's x to the x. The two numbers need to
be the same. Oh. Oh, so 2, dude. Slow
down. 2 ^ 2ar is 4. Way too small. And 3
cubed. 3 * 3 * 3 is 27. Too big. Okay,
but the answer has to be somewhere
between 2 and 3. That's at least a rule
we've proved now. But the problem is we
can't solve this like this. X is mad
stuck. So, we need to use a secret
little math weapon. The natural log.
Natural log is badass. It helps us pull
the exponent down into something we can
handle. So, if we take the natural log
of both sides, the natural log of x to
the x [music] brings the exponent down
and out front. So we get x ln x is equal
to ln25. Now I would still probably
guess and check values between 2 and
three on this but technically you need
to use another secret weapon to solve
this. The lambert w function and that
yanni lets you go uh boop boop boop and
uh boop boop boop x is like 2.947. Want
more SAT hacks? Click the video below.

Get Our Mobile App

Tricky SAT question..

Transcription