Sir/Ma'm,

I have a query that if x^{x} = 0 => x = ?

I am joy, a teacher teaching Maths at the secondary level and while solving a sum came to this stage when i got
x^{x} (1 + log x) = 0, by which we can conclude that x^{x} = 0 or 1 + log x = 0. If x^{x} = 0, than what should be the value of x? I feel that the value of x should then be 0 (zero) but then how do I explain this to the students as we also know that anything to the power of 0 is 1 but here 0 raised to 0 is 1. If this is not defined then how do I explain this ?

Please help me as i have got to explain this to the children.

Thank you.

Truly yours,

Joy

Hi Joy,
In an answer to a previous question about 0^{0} the conclusion is that it is best to leave 0^{0} undefined. In your problem, however, the status of 0^{0} is not an issue.

Since log x is only defined for x positive, your expression x^{x} (1 + log x) is only defined for x positive. When x is positive x^{x} is also positive so the only solution to x^{x} (1 + log x) = 0 is the solution you found by solving 1 + log x = 0.

Cheers,

Penny