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The real solutions of x = ax

Published online by Cambridge University Press:  22 June 2022

A. F. Beardon
A. F. Beardon*
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB email: afb@dpmms.cam.ac.uk
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We denote the real logarithm of a positive number a by ln a, so that ax = exp (x ln a), and we shall discuss what is known about the real solutions x of the equation (1)

$$x = {a^x},\;\,a > 0.$$
First, as exp t > 0 for all real t, each real solution x of (1) is positive.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 566 , July 2022 , pp. 206 - 211
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Copyright
© The Authors, 2022 Published by Cambridge University Press on behalf of The Mathematical Association

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