Question

3^x=4^y=36,则2/x+1/y等于多少?

Answer 1

∵3^x=4^y=36

∴x=log(3)(36)

y=log(4)(36)

∴2/x+1/y

=2/log(3)(36) + 1/log(4)(36)

根据换底公式 可知1/log(3)(36)=log(36)(3)

同理1/log(4)(36)=log(36)(4)

∴2/x+1/y=2*log(36)(3)+log(36)(4)

=log(36)(9)+log(36)(4)

=log(36)(36)

=1.