This applet shows the intersections of the graphs of [math]a^x[/math] and [math]log_a\left(x\right)[/math].[br][br]Please see [url=https://publikacio.uni-eszterhazy.hu/2867/1/AMI_43_from159to170.pdf]reference 1[/url] and [url=https://www.math.sinica.edu.tw/media/pdf/d284/28402.pdf]reference 2[/url] for details.