We just started logarithms and exponential functions, and I'm kind of getting the gist but not really. Here is what I tried on one of the homework problems:

Question

2^X=4^X+1

1)2^X=(2^2)^X+1
2)x=x+1
3)0=1 or no solutions

I wasn't sure what to do between steps 1 and 2. Thanks!!

Answer 1

If the question is the way you typed it, it is a nasty question.
I am pretty sure you meant
2^x = 4^(x+1)

did you notice that both bases are powers of 2 ?
2^x = (2^2)^(x+1)
2^x = 2^(2x+2)
then 2x + 2 = x
x = -2

Answer 2

I see where the extra step was! Thanks so much!