3^a=4^b=36,求2/a=1/b的值

3^a=4^b=36,求2/a=1/b的值
3^a=4^b=36,求2/a=1/b的值

3^a=4^b=36,求2/a=1/b的值
法一：3^a=4^b=36 ==>a=log3 36=log3 4+log3 9=2log3 2+2 ==>b=log4 36=log4 4+log4 9=1+log2 3 ==>2/a+1/b=1/(1+log3 2)+1/(1+log2 3)=lg3/(lg2+lg3)+lg2/(lg2+lg3)=1 法二：因为a3^a=36,4^b=36.所以：a=lg36/lg3=2lg6/lg3,b=lg36/lg4=lg6/lg2 2/a+1/b =(a+2b)/(ab) =(2lg6/lg3+2lg6/lg2)/[2lg6×lg6/(gl2×lg3)] =[2lg6(lg2+lg3)/lg2×lg3]×[lg2×lg3/(2lg6×lg6)] =2lg6(lg2+lg3)/(2lg6×lg6) =(lg2+lg3)/lg6 =lg6/lg6 =1