Blogger blog ranking fast?

How to rank fast with high searching keywords but low competition with blogger blog site withou headache Black Hat SEO?

Dose the domain authority matters more than the page authority?

If i ran some keywords in the moz bar and it tells me in the google search that all the results have high domain authority and low page authority and i just create blogger blog in that keywords dose this help me in ranking fast ?

Try it for different keywords and see for yourself. SEO is more than just domain authority and page authority. You need to identify the best keywords. Low competition keywords would rank quicker and better.

googlebis said:

Dose the domain authority matters more than the page authority?

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Nope. It's quite the opposite. A site with 50 PA and 15 DA can outrank sites with 70+ DA.

and i just create blogger blog in that keywords dose this help me in ranking fast ?

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It won't. Blogger blogs can't rank any better than a self-hosted WordPress site.

How to rank fast with high searching keywords but low competition with ... withou headache Black Hat SEO?

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It's not head-ache and we do this all day every day. If it brings head-ache for you, better outsource the task to the experts or buy links from the https://www.blackhatworld.com/forums/seo-packages.206/.

SpoonFeeder said:

It won't. Blogger blogs can't rank any better than a self-hosted WordPress site.

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now you just shattered some 7$ WSO Ebooks out there..

The answer would apply to any blog platform. Just because you use blogger doesn't mean things will move faster, regardless of some would believe.
But for the sake of things, a few simple steps considering you did mention low competition keywords would be:

1) 4-5 web 2.0 properties with 2-3 filler articles each.
1.a) If possible and you have time on your hands ( you should ) do some simple blog commenting links pointing to each of those web 2.0

2) Say you have 3 or 4 main low competition keywords. Create one VERY GOOD article for each keyword around 1000 words and up about that topic. By this I'm talking about REAL GOOD articles, no spun or etc. Should be documented, well written, keyword density enough to make a difference. You will only be writing it once, so make it worth it.

3) Get some patiente. You can't buy that here, so better find it in you. By patiente i mean at least 10 days or so before you see anything noticeable.
4) You think those pages will get you any income in the future? Invest a few bucks in them buying some good links from the BST threads here. Just a few bucks to get them rolling.
5) Find 2-3 forums somewhat relevant to your niche. Post in them until they let you use a signature and use the signature. Don't over do this. As I sad, 2-3 will be enough.
6) Submit your maine domain to 5-10 tops web directories. I literally mean 5-10,not 100, 1000 etc.

These are NOT the best advices you can get, but it will help you get things rolling a little.