An Easy Exponential Equation | Stanford Mathematics Tournament

[wkbj]

Interesting problem. I simplified cases 2 and 3 by observing that x^2-10x+26=(x-5)^2+1. Thus, since x is real, x^2-10x+26 cannot be less than 1.

[gdefus]

The base of a power function must always be greater than zero if we work with real numbers.
f(x)^g(x) => f(x) > 0

[jax]

My first thought was anything^0 = 1

Plugged in 1 as x, and got it

[josipbroztito]

We cannot consider third case because its not a defined

[mcwulf]

In my haste I forgot about (3). Nice little puzzle.

[mohmohanplaylist]

When stating the cases Should mention that the exponent and the base must not be equal to zero at the same time.

[Alex.]

Why he doesn't consider complex solutions?

[cadennar]

Isn’t there a case when the base and the exponent is 0 because that equals 1?
Did he forget or is there a reason?

[unknown-clyi]

The solutions are odd numbers lol. Never expected

[supu]

Mind your disition has a similar problem solved. 👍