Question

Answer the question in the photo , its the easy one please help me ;((

Answer 1

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