33.不用计算器,证明：[log6]^2=/=log3*log12
问题描述：
33.不用计算器,证明：[log6]^2=/=log3*log12
答
[log6]^2= [log2+log3]^2= [log2]^2+2*[log2]*[log3]+[log3]^2log3*log12= log3*[2*log2 + log3]= 2*[log2]*[log3]+[log3]^2[log6]^2 - log3*log12= [log2]^2=/= 0故 [log6]^2=/=log3*log12