## Quant Question Of The Day: 155

**Algebra**

**How many real numbers x are solutions to the following equation?**

**2017 ^{x} + 2018^{x} = 2019^{x . }**

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Quant question of the day, Question of the day

**How many real numbers x are solutions to the following equation?**

**2017 ^{x} + 2018^{x} = 2019^{x . }**

**Rewrite the equation as (2017/2018) ^{x} + (2017/2018)^{x} = 1. The left side is strictly decreasing in x, so there cannot be more than one solution. On the other hand, the left side equals 2 > 1 when x = 0 and goes to 0 when x is very large, so it must equal 1 somewhere in between. Therefore, there is one solution.**

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