MathDB

EZ logarithm

Source: 2023 AIME I #2

February 8, 2023

AMCAIMEnumber theoryrelatively primelogarithms

Problem Statement

\sqrt{\log_bn}=\log_b\sqrt n

and

b\log_bn=\log_bbn,

then the value of

n

is equal to

\frac jk,

where

j

and

k

are relatively prime. What is

j+k