MathDB
Logarithm

Source: 2003 National High School Mathematics League, Exam One, Problem 10

March 16, 2020
logarithms

Problem Statement

a,b,c,da,b,c,d are positive integers, and logab=32,logcd=54\log_{a}b=\frac{3}{2},\log_{c}d=\frac{5}{4}. If ac=9a-c=9, then bd=b-d=________.