An atm Q?

Algebra Level 3

5 x + 5 x − 1 + 5 x − 2 + 5 x − 2 + 5 x − 3 + 5 x − 3 + 5 x − 5 + 5 x − 5 + 5 x − 5 = 101325 5^x + 5^{x - 1} + 5^{x - 2} + 5^{x - 2} + 5^{x - 3} + 5^{x - 3} + 5^{x - 5} + 5^{x - 5} + 5^{x - 5} = 101325

Solve for positive integer x x .


The answer is 7.

Yajat Shamji by Yajat Shamji , 16, United Kingdom

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1 solution

Let's 5 x − 5 5^{x-5} be a: 3125 a + 625 a + 2 × 125 a + 2 × 25 a + 3 a = 4053 a 3125a+625a+2\times125a+2\times25a+3a=4053a 4053 a = 101325 ⟹ a = 25 4053a=101325\implies a=25 5 x − 5 = 25 ⟹ x − 5 = 2 ⟹ x = 7 5^{x-5}=25\implies x-5=2\implies x=7

1 Helpful 1 Interesting 1 Brilliant 0 Confused

lol I missed one number

A Former Brilliant Member - 10 months ago

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