How to reduce small logo size and keep the image clear with good resolution?

Can you tell me how to reduce an image logo to smaller size and still
maintain high resolution clarity?

I have a small logo in one layer.
I want to reduce the size of logo relative to the rest of picture.

However, when I try to reduce the logo size from 1/2" to 1/8" the resolution
and clarity of the logo becomes very poor. In particular, I cannot read all
the wordings.

How can I reduce the size of logo and still keep high resolution quality?
Thank you, Jo