If $a>1$, the number of values of $x$ for which $\log_a x=x=a^x$

58 Views Asked by At

My book says $0$ solutions for $a>1$, but as $1<a<1.44 \text{ (approx)}$ that graphs intersect at two positions. So is the answer $2$ for $1<a<1.44$, and $0$ for $a>1.44$.

I'm not sure about the exact value of the upper limit of $a$. Could you please find out the exact value? (If it is a irrational number, is it possible to write in any known forms like root or logarithm?)