There exist positive intergers A,B,C with no common factor greater than 1, such that Alogbase200(5) + Blogbase200(2)=C, find A,B,C
Follow Math Help Forum on Facebook and Google+
Originally Posted by KingV15 There exist positive intergers A,B,C with no common factor greater than 1, such that Alogbase200(5) + Blogbase200(2)=C, find A,B,C 1. Use the base 200 with your equation: $\displaystyle A\log_{200}(5) + B\log_{200}(2)=C$ $\displaystyle 5^A \cdot 2^B = 200^C$ $\displaystyle 5^A \cdot 2^B = (5^2 \cdot 2^3)^C$ Therefore: $\displaystyle A = 2C~\wedge~B=3C$ Choose a number for C.
View Tag Cloud