On The Irrationality Measure Of Log3

Letαbe an irrational real number. If for anyε> 0, there exists q0(ε)>0, such that for all integers p and q with q≥qo(ε), then the real numberμ> 0 is said to be an irrationality measure of a.In this work, we mainly prove the irrationality measure of log 3. Many people are studying the problem. The most recently results areμ(log 3)=8.616 by Rhin in 1987 andμ(log3)≤5.125 by Salikhov in 2007.In this paper, we getμ(log3)=5.1163. Our computation use a method con-cerned the integer transfinite diameter,LLL algorithm and semi-infinite linear pro-gramming.