How do I add two numbers with the same base but different exponents?

The problem I've been given is the following:

16 + 2^x = 2^(x+1)

I know this simplifies to 2^4 + 2^x = 2^(x+1) but then I'm stuck.

Thanks in advance!

1 Answer
Apr 20, 2018

I tried this:

Explanation:

Here I would write:

2^(x+1)=2^x*2^1

so that your equation becomes:

2^4+2^x=2^x*2^1
rearrange:
2^4=2^x*2^1-2^x
2^4=2^x(2-1)
2^4=2^x*1
then:
2^x=2^4/1
or:
2^4=2^x
so that:
x=4