# Math Help - Find Values Log

1. ## Find Values Log

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

2. 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:

$A\log_{200}(5) + B\log_{200}(2)=C$

$5^A \cdot 2^B = 200^C$

$5^A \cdot 2^B = (5^2 \cdot 2^3)^C$

Therefore:

$A = 2C~\wedge~B=3C$

Choose a number for C.