Algebra 2/Trig

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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:
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!!

  • Algebra 2/Trig -

    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

  • Algebra 2/Trig -

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

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