Can I use a Nikon F objective with a Olympus OM-D E-M10?

I want to buy a Olympus OM-D E-10 with a 14-42mm lens for travelling (lighter than my Nikon D7000).

My question is, is there any way (“which makes sense”) to use my Tamron SP 70-300mm F/4-5.6 lens for Nikon with this Olympus OM-D E-10 ?

Or should I better spend more money for a bigger standard lens like 14-150mm?

But I would prefer the first, if there is any “good” way.