floor problem1

Algebra Level 3

⌊ 2 x ⌋ + ⌊ 3 x ⌋ = ⌊ 5 x ⌋ + 1 \large \lfloor 2^x\rfloor + \lfloor 3^x \rfloor = \lfloor 5^x \rfloor+1

Find the integer value of x x satisfying the equation above.

Notation: ⌊ ⋅ ⌋ \lfloor \cdot \rfloor denotes the floor function .


The answer is 0.

Aly Ahmed by Aly Ahmed , 34, Egypt

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2 solutions

Chew-Seong Cheong
May 30, 2018

The solution is a range 0 ≤ x < log ⁡ 5 2 0 \le x < \log_5 2 , where the L H S = R H S = 2 LHS = RHS = 2 .

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Zico Quintina
May 29, 2018

0 0 is a solution by inspection. There is a second solution, x ≈ 0.30379398... x \approx 0.30379398... but I don't believe it can be found algebraically.

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