已知a,b满足6^a=2010,335^b=2010,求1/a+1/b的值

Question

已知a,b满足6^a=2010,335^b=2010,求1/a+1/b的值

Answer 1

6^a=2010 a=log6(2010) 1/a=log2010(6)
335^b=2010 b=log335(2010) 1/b=log2010(335)
1/a+1/b=log2010(6)+log2010(335)=log2010(6×335)=log2010(2010)=1