SOLUTION: For what value(s) of k does the equation x^1/logx=k have a solution?

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Question 1008787: For what value(s) of k does the equation x^1/logx=k have a solution?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


x cannot be 1 since the denominator of the exponent
would be 0.

Take logs of both sides:



Use a rule of logs to write the exponent as a coefficient
of a log:







matrix%282%2C3%2C%0D%0A%22%22%2C%22%22%2C%22%22%2C%0D%0A%0D%0A10%2C%22%22=%22%22%2Ck%29

Substitute for k in







This will be true for every allowable value of x

Thus the equation



has a solution for every positive value of x except 1

That is, for all x ∈ {x|0 < x < 1 or x > 1}

 (0,1) U (1, ∞)

Edwin