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How can I do this advanced math problem?

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.

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Answer #1

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?

Answer #2

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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