Is it possible to solve $a^{-x} = \log_a(x)$ with $x$ in terms of $a$?
2026-05-05 13:39:36.1777988376
General solution of $a^{-x} = \log_a(x)$
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As was said - it cannot be solved analytically. But the function $x=x(a)$ can be solved for numerically and plotted.
The function is defined only for $a>0$. It has a discontinuity at $a=1$. It has a maximum at around $a\approx1.8$ where $x\approx1.3$. As $a\to\infty$, $x$ goes to $1$