To solve the equation (5^{x+1} - 2*5^{x-1} - 23 = 0), we can first simplify the equation:
(5^{x+1} = 5^x 5 = 55^x)
(25^{x-1} = 25^x/5 = 2/5 * 5^x)
So the equation becomes:
(55^x - 2/55^x - 23 = 0)
Simplify further:
(5^x (5 - 2/5) - 23 = 0)
(5^x (25/5 - 2/5) - 23 = 0)
(5^x (23/5) - 23 = 0)
(23/5 * 5^x = 23)
(5^x = 5)
Now we have a simple exponential equation where the base is the same on both sides. Therefore, (x = 1).
To solve the equation (5^{x+1} - 2*5^{x-1} - 23 = 0), we can first simplify the equation:
(5^{x+1} = 5^x 5 = 55^x)
(25^{x-1} = 25^x/5 = 2/5 * 5^x)
So the equation becomes:
(55^x - 2/55^x - 23 = 0)
Simplify further:
(5^x (5 - 2/5) - 23 = 0)
(5^x (25/5 - 2/5) - 23 = 0)
(5^x (23/5) - 23 = 0)
(23/5 * 5^x = 23)
(5^x = 5)
Now we have a simple exponential equation where the base is the same on both sides. Therefore, (x = 1).