Solutions with a Floor

★ 5/10functions number theory algebra Logarithms Casework

Problem

Let $\lfloor x \rfloor$ denote the greatest integer not exceeding $x$ . How many real solutions does the equation

2^x - 2\lfloor x \rfloor - 1 = 0

have?

Answer

Solution

Difficulty	5/10
Topics	functions, number theory, algebra, Logarithms, Casework

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