Here's how I would achieve that effect:
1) Create a BW Effects layer, and select the mode that gives the most pleasing effect.
2) Edit>Copy Merged, then paste that into a new alpha channel
3) Invert the alpha channel
4) Delete or disable the bw effects layer
5) Select the active pixels (Control key (PC) or the Command key (Mac) while you single click on the alpha channel in the channels panel)
6) Create a new solid color layer using the purple you used above

The active selection of the alpha channel will automatically be applied as a transparency mask. That SHOULD do it. Good luck.

Use the image as an alpha mask. Take this black and white "logo" as an example:

1. Select All and Copy (or Copy Merged if you have multiple layers).

2. Create a new mask with the "New Layer Mask" button in the Layers panel (either on the your logo layer or a group containing your logo if it has multiple layers).

3. Alt+Click the mask thumbnail to edit the mask (your canvas should turn completely white), then paste the image you previously copied. Click the layers thumbnail to finish editing the mask.

4. As you can see, the semi-transparency defined by the various levels of gray are still gray in color too. If that isn't what you want then select all and fill the layer completely with white (or whatever color you want the logo to be).

Your now transparent logo: