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# Finding the point of intersection of this graph?

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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 E​9) 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)?

Apr 7, 2019
edited by Guest  Apr 7, 2019
edited by Guest  Apr 7, 2019

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

1252x-1  = 25x + 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   Apr 7, 2019