Pigols and Egols

Algebra Level pending

A pigol (PIE gol) is defined as being equal to ⌊ 10 99 π ⌋ \left\lfloor { 10 }^{ 99 }\pi \right\rfloor . An egol (EE gol) is defined as being the somewhat smaller ⌊ 10 99 e ⌋ \left\lfloor { 10 }^{ 99 }e \right\rfloor .

When the product of a pigol and an egol are written in the form 10 x { 10 }^{ x } , what are the first three digits after the decimal point of x x ?


The answer is 931.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

log ⁡ 10 ( 10 198 e π ) \log _{ 10 }{ { (10 }^{ 198 }e\pi ) } = 198. 931 4 … 198.\boxed{931}4\dots

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