4 ^(1+2x)=1024 how do I express each side as a power of the same base and then equate exponents?

I'll help a bit!

So, we need to have the same base on either side, like this:

Essentially, we need to find the factors of 1024:

So then, we can write it as:

(As there are 5 4's in the factorization)

So, let's solve!

First step, use the Equality of Bases Property:

It states that:

Then:

So, continuing on:

Hope this helps!

(hope this also answers your question)

P.S. Ask me if you have any more questions, and remember to wash your hands!