SOLUTION: Solve: 16^(x) + 4^(x+1)

SOLUTION: Solve: 16^(x) + 4^(x+1) - 3 = 0 Thanks!

Question 913163: Solve: 16^(x) + 4^(x+1) - 3 = 0
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let

Use the quadratic formula to get or

The steps for the quadratic formula are lengthy and I feel they would clutter up this solution page. Let me know if you need to see the steps to getting those solutions for z.

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The solutions in terms of z are or

We ultimately want solutions in terms of x.

Plug in the first solution for z to get the first solution for x.

So the first solution is

Using a calculator, we get log(-2+sqrt(7))/log(4) = -0.3154747

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Plug in the second solution for z to get the second solution for x.

So the second solution is ; however, notice how is negative. That means the log of this value is undefined. So log(-2-sqrt(7)) = log(-4.64575) = Undefined

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Final Answer:

The only exact solution is

The only approximate solution is

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim

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