Question

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

Answer 1

Answer:

I'll help a bit!

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

$EX:4^{7} =4^{x}$

Essentially, we need to find the factors of 1024:

$1024=4*4*4*4*4$

So then, we can write it as:

$4^{1+2x} =4^{5}$

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

So, let's solve!

First step, use the Equality of Bases Property:

It states that:

$x^{v} =x^{c}$

Then:

$v=c$

So, continuing on:

$1+2x=5\\2x=4\\x=2$

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!