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How can i do this advanced math problem?

Lilly Asked by beauty_queen_4_lyphe 29 days ago, 2 answers.

Anyone knows how to do this problem?
I need help and fast.
Solve for x.
2^2x-10(2^x)+16=0

Thanks in advance.

Clearing the Gene Pool Answered by bimjob on Oct 24, 2009, 05:50PM
3263 answers

Homework questions ARE allowed, but this one is a tad confusing.
(Although I do not think anyone here is going to do your homework, we can help and give hints.)

Is it (2 raised to the 2x power) minus (10 times the quantity 2 to the x power) + 16 = 0
In other words subbing 'n' for 'x' is this what you are asking

2²ⁿ - 10(2ⁿ) + 16 = 0

Could the answer be simplified and solved as follows???
(2²)ⁿ - 20ⁿ + 16 = 0
(4)ⁿ - 20ⁿ + 16 - 16 = 0 - 16
4ⁿ - 20ⁿ = -16
-16ⁿ = -16
Therefore n=1

I really don't know if that is correct math. It has been to long since I played with exponents.

I hope this helped, but I'm not sure...
Good Luck!!
(I changed 'x' to 'n' because ALT codes have a superscript 'n' but not 'x')
Beauty Queen, let me know if this was correct, will you please?

Answered by kusari on Oct 27, 2009, 10:25PM
38 answers

sorry bimjob but just part of your working was wrong. The last 2 steps to be precise.
Oh! And the first step. But good try. This problem is not as tricky as it seems. Let me show you.

2^(2x) - 10(2^x) + 16 = 0
(2^x)^2 - 10(2^x) + 16 = 0 [ Then make the substitution y = 2^x ]
y^2 - 10y + 16 = 0
(y -2)(y-8) = 0
therefore y = 2 or y =8
this means that 2^x = 2 or 2^x = 8
therefore x = 1 or x = 3.

There you go. =)

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