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

In an answer to a previous question about 0⁰ the conclusion is that it is best to leave 0⁰ undefined. In your problem, however, the status of 0⁰ 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.