I need to prove that \({125^{2y-1} = 25^{y+4}}\) by graphing it.

I graphed it here.

However, I can't seem to find the point of intersection?

Graphing it on my graphing calculator, I got **(2.75, 2.72958 E9)** as the point of intersection. However, how is that graphically possible since I don't see that point anywhere (both on the graph on my calculator and on desmos)?

Guest Apr 7, 2019

edited by
Guest
Apr 7, 2019

edited by Guest Apr 7, 2019

edited by Guest Apr 7, 2019

#1**0 **

Well......let's see if this has a solution....we have that

125^{2x-1} = 25^{x + 4}

(5^3)^{2x- 1} = (5^2)^{x + 4}

5^(6x - 3) = 5^(2x + 8) we have the bases the same...so....we can solve for the exponents

6x - 3 = 2x + 8

4x = 11

x = 11/4 = 2.75

The problem is probably that you didn't set the y scale high enough in Desmos

We need it to be at least 25^(2.75 + 4) ≈ 2,729,575,167 ≈ 2800000000

[ I set the x scale for 0 to 3 and the y scale for 0 to 2800000000 ...no commas !!!]

See the Desmos graph here : https://www.desmos.com/calculator/emuwj0rwgf

CPhill Apr 7, 2019