若a^2=3^b=36,则1/a+1/b=?

Question

若a^2=3^b=36,则1/a+1/b=?

Answer 1

2^a=3^b=36
a=log2(36)=lg36/lg2
b=log3(36)=lg36/lg3
1/a+1/b=lg2/lg36+ lg3/lg36 = (lg2+lg3) / lg36 =lg6 / lg6^2 = lg6 / (2lg6) =1/2