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Math Help - Solve for X... Please Help

  1. #1
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    Solve for X... Please Help

    Sorry, I couldn't paste properly from Word. So I want to Print Screen it.

    Here's the link:

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

    Can you solve it for me, step-by-step?

    Thanks.
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  2. #2
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    Quote Originally Posted by iwanttogotouni View Post
    Sorry, I couldn't paste properly from Word. So I want to Print Screen it.

    Here's the link:

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

    Can you solve it for me, step-by-step?

    Thanks.
      x = log_2 \sqrt[8] 2

     x = log_2 (2^{\frac{1}{8}})

    Using the log law  log (x^y) = y log x

     x = \frac{1}{8} log_2 (2)

    Using the log law  log_a (a) = 1

     x = \frac{1}{8}
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  3. #3
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    Wow... apparently the answer on my sheet is x = 3.5.

    I'm not saying you're wrong. I'll take a picture, and upload it, too. So you can see my teacher's logic.
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  5. #5
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    Quote Originally Posted by iwanttogotouni View Post
    The question you gave at the beginning says  log_2 (\sqrt[8] 2) . The question shown here is  log_2 (8\sqrt2) . There is a huge difference there.

    Ok for this question

     x = log_2 (8\sqrt2) = log_2 (2^3 \times 2^{\frac{1}{2}})

    Using the log law  log (x \times y) = log (x) + log (y)

     x = log_2 (2^3) + log_2 (2^{\frac{1}{2}})

    Using the log law  log (x^y) = y log (x)

     x = 3 log_2 (2) + \frac{1}{2} log_2 (2)

    Using the log law  log_a (a) = 1

     x = 3 + \frac{1}{2} = 3.5 Which is the answer you have.
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  6. #6
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    OK. So having that number to the side, and not in the top-left is a huge difference. THANKS!

    Edit: Where does the 1/2 come from? I'm sorry, I'm a hands-on learner.
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  7. #7
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    Quote Originally Posted by iwanttogotouni View Post
    OK. So having that number to the side, and not in the top-left is a huge difference. THANKS!

    Edit: Where does the 1/2 come from? I'm sorry, I'm a hands-on learner.
    On the side means 8 times square root 2. On the top left means the 8th root of 2.

    The square root of two can also be written as  2^{\frac{1}{2}} Similarly, the cube root of two is written as  2^{\frac{1}{3}} . Generally the mth root of x is written as  x^{\frac{1}{m}} . This is just the notation used.
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  8. #8
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    Thanks!
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