Graph Intersections

Geometry Level 2

How many integer solutions are there to the graphs y = x 2 y=x^2 and y = 2 x y=2^x ?


The answer is 2.

Ephram Chun by Ephram Chun , 16, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

James Watson
Jan 27, 2021

there are 3 real solutions to this. however, only 2 are integer solutions which are ( 2 , 4 ) , ( 4 , 16 ) (2,4), (4,16) so the answer is 2 \boxed{2} .

(P.S the other real solution is ( − 2 W ( − ln ⁡ ( 2 ) 2 ) ln ⁡ ( 2 ) , e − 2 W ( ln ⁡ ( 2 ) 2 ) ) \left( -\frac{2W\left(-\frac{\ln(2)}{2}\right)}{\ln(2)}, e^{-2W \left(\frac{\ln(2)}{2}\right)}\right) where W ( x ) W(x) is the lambert W function)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Vijay Simha
Jan 26, 2021

By inspection (2,4) and (4,16) are two solutions.

0 Helpful 0 Interesting 0 Brilliant 2 Confused

How do you know no other solution exists?

Pi Han Goh - 4 months, 2 weeks ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...