MathDB

2

Part of 2023 AIME

Problems(2)

EZ logarithm

Source: 2023 AIME I #2

2/8/2023
If log⁡bn=log⁡bn\sqrt{\log_bn}=\log_b\sqrt n and blog⁡bn=log⁡bbn,b\log_bn=\log_bbn, then the value of nn is equal to jk,\frac jk, where jj and kk are relatively prime. What is j+kj+k?
AMCAIMEnumber theoryrelatively primelogarithms
base eighthgie esab

Source: 2023 AIME II Problem #2

2/16/2023
Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than 10001000 that is a palindrome both when written in base ten and when written in base eight, such as 292=444eight292=444_{\text{eight}}.
AMCAIMEAIME II