I have been asked to find the angle between the curves
$y=2^x\ln x$
$y=x^{2x}-1$
But I'm having a tough time finding the point of intersection itself.
By trial and error, one could substitute 0,1,e....and find that 1 satisfies both the curves, but I think there might be more than one point of intersection.
My attempt to trace the graph was also futile.( I thought I could prove that the curves won't intersect again)
in other words, find the possible points of intersection of the aforementioned curves
Considering the function $$f(x)=2^x\log(x)-(x^{2x}-1)$$ it cancels at $x=1$.
At this point, the first derivative also cancels and the second derivative test reveals that this is a maximum $\big(f''(1)=-8+4\log(2)<0\big)$