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

Question

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!

1134 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-20T12:49:00

I tried this:

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#