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I second Kyle's answer (just upvoted it) - and downvote any of the subdomain recommendations.
There is a running myth that subdomains hold the same SEO value as subdirectories... Unfortunately Google reps have confused a lot of people about this topic.
The subdomain option is only advisable if your site is an absolute beast. A good example of this is blog.HubSpot.com - their subdomain blog ranks really really well. However, they have a small army of marketers publishing, promoting, and sharing their content daily. They have also had several rounds of funding to fuel this authority they're gaining on the subdomain. Unless that sounds like you, avoid the subdomain strategy.
Compare that to the average blog, and it's a clear choice to use the directory over the subdomain, so you're not splitting authority across two domains. I don't care what Google has published, the data and the facts show time and time again that for 97%+ of blogs, subdirectories get much more SEO love than subdomains do. The reason is mechanical in nature. Think about it. Two domains equals twice the links necessary to get the same authority on one root domain. After optimizing hundreds of sites since 2005, I've found this to hold true with rare exception (the blogs that are beasts).
Follow respectable SEO's (like moz.com) who have case studies and data to show what's currently working on sites that are similar in size to yours. That's where you'll find the answer.