AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_7 / For how many integers n does the expression√((log(n²)−(logn)²)/(logn−3))represent a real number, where log denotes the base 10 logarithm?

Problem

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For how many integers n does the expression√((log(n²)−(logn)²)/(logn−3))represent a real number, where log denotes the base 10 logarithm?

For how many integers $n$ does the expression\[\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}}\]represent a real number, where log denotes the base $10$ logarithm?

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Source and history

upstream_id / Original problem ID

https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_7

task_id

22a999e1-f4e2-5cb0-baac-5c87cd952f4f

task_key

default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f7

task_revision_id

2

config / split

default / train

Official source

initial import