9514 1404 393
Explanation:
The problem statement tells you what to do.
25^(n-1) +125 -6·5^n = 0 . . . . . subtract 6·5^n
(5^2)^(n-1) -6·5^n +125 = 0 . . . . express 25 as a power of 5
5^(2n-2) -6·5^n +125 = 0 . . . . . eliminate the double layer of exponent
(5^-2)(5^n)^2 -6·5^n +125 = 0 . . . . . use 5^n where possible
(1/25)y^2 -6y +125 = 0 . . . . . . . substitute y = 5^n
y^2 -150n +3125 = 0 . . . . . . . . . multiply by 25
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The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
