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Math Help - One last exponent question~ Can someone check the answer, please?

  1. #1
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    One last exponent question~ Can someone check the answer, please?

    With the help of the forum, I've gone through many more exponent exercises. But I have one more questions.

    Problem with this one is that I do not know the answer, but I assume that the answer much be a simple whole number - all the other answers for this section are - but my solution doesn't seem to be right.

    Problem

    2^(x)+8*2^(-x)=9

    I started out by multiplying both sides by 2^(x)... and simplified. I ended up with 20^x=18^x

    any thoughts?!?
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  2. #2
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    Re: One last exponent question~ Can someone check the answer, please?

    Quote Originally Posted by conpark View Post
    Problem
    2^(x)+8*2^(-x)=9
    I started out by multiplying both sides by 2^(x)... and simplified. I ended up with 20^x=18^x
    No you don't.
    You have 2^{2x}+8=9\cdot 2^x.

    Please learn some basic LaTex.
    [TEX]2^{2x}+8=9\cdot 2^x[/TEX]
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  3. #3
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    Re: One last exponent question~ Can someone check the answer, please?

    Hello, conpark!

    Problem with this one is that I do not know the answer. **

    . . 2^x+8\!\cdot\!2^{-x}\:=\:9

    Multiply by 2^x\!:\;\;2^{2x} + 8 \:=\:9\!\cdot\!2^x \quad\Rightarrow\quad 2^{2x}- 9\!\cdot\!2^x + 8 \:=\:0


    Factor: . \left(2^x - 1\right)\left(2^x - 8\right) \:=\:0


    Solve the resulting two equations:

    . . 2^x - 1 \:=\:0 \quad\Rightarrow\quad 2^x \:=\:1 \quad\Rightarrow\quad x \:=\:0

    . . 2^x - 8 \:=\:0 \quad\Rightarrow\quad 2^x \:=\:8 \quad\Rightarrow\quad x \:=\:3


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    ** It's difficult to solve a problem when we don't know the answer.

    At the start of a trip, my odometer read 23,400 miles.
    At the end of the trip, it read 23,700 miles.
    I'd like to know how far I drove . . . but I don't know the answer.

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