∵4^X=6
∴X=log 4 (6) 【对数定义】
= log 6 (6) / log 6 (4) 【换底公式】
= 1/log 6 (4)
∵9^Y=6
∴y=log 9 (6) 【对数定义】
= log 6 (9)/log 6 (9) 【换底公式】
=1/log 6 (9)
∴1/X+1/Y
= 1/{1/log 6 (4)} + 1/{1/log 6 (9)}
= log 6 (4) + log 6 (9)
= log 6 (4*9)
= log 6 (6^2)
= 2
∵4^X=6
∴X=log 4 (6) 【对数定义】
= log 6 (6) / log 6 (4) 【换底公式】
= 1/log 6 (4)
∵9^Y=6
∴y=log 9 (6) 【对数定义】
= log 6 (9)/log 6 (9) 【换底公式】
=1/log 6 (9)
∴1/X+1/Y
= 1/{1/log 6 (4)} + 1/{1/log 6 (9)}
= log 6 (4) + log 6 (9)
= log 6 (4*9)
= log 6 (6^2)
= 2