SOLUTION: what is the value of x? 4^20+4^20=2^x

Question 177704: what is the value of x?
4^20+4^20=2^x
Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!
To solve this problem you need to be a little clever. The first thing to notice is that everything on the left hand side is a power of 4 while everything on the right hand side is a power of 2. It would be nice if they were the same, specifically 2, since that's the side with the variable. Can we change into base 2? Sure, since . So we have that

And because of the rules of exponents, we have that

So we can rewrite the equation:

Now, we combine like terms on the left hand side:

What is ? Well, all we're doing is multiplying by another 2, so it's just . So,

So x=41.
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