MathDB

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Part of 2000 AIME Problems

Problems(2)

Powers of 10

Source:

1/5/2007
Find the least positive integer nn such that no matter how 10n10^{n} is expressed as the product of any two positive integers, at least one of these two integers contains the digit 0.0.
Simple Logarithms

Source:

12/8/2005
The number 2log⁡420006+3log⁡520006 \frac 2{\log_4{2000^6}}+\frac 3{\log_5{2000^6}} can be written as mn\frac mn where mm and nn are relatively prime positive integers. Find m+n.m+n.
logarithmsnumber theoryrelatively prime