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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- Mar 12th 2010, 07:47 PMiwanttogotouniSolve 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. - Mar 12th 2010, 08:04 PMGusbob
$\displaystyle x = log_2 \sqrt[8] 2$

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

Using the log law $\displaystyle log (x^y) = y log x $

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

Using the log law $\displaystyle log_a (a) = 1 $

$\displaystyle x = \frac{1}{8} $ - Mar 12th 2010, 08:08 PMiwanttogotouni
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. - Mar 12th 2010, 08:16 PMiwanttogotouni
- Mar 12th 2010, 08:24 PMGusbob
The question you gave at the beginning says $\displaystyle log_2 (\sqrt[8] 2) $. The question shown here is $\displaystyle log_2 (8\sqrt2) $. There is a huge difference there.

Ok for this question

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

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

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

Using the log law $\displaystyle log (x^y) = y log (x) $

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

Using the log law $\displaystyle log_a (a) = 1 $

$\displaystyle x = 3 + \frac{1}{2} = 3.5 $ Which is the answer you have. - Mar 12th 2010, 08:25 PMiwanttogotouni
OK. So having that number to the side, and not in the top-left is a huge difference. THANKS!

Edit: Where does the $\displaystyle 1/2$ come from? I'm sorry, I'm a hands-on learner. - Mar 13th 2010, 01:36 AMGusbob
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 $\displaystyle 2^{\frac{1}{2}}$ Similarly, the cube root of two is written as $\displaystyle 2^{\frac{1}{3}} $. Generally the mth root of x is written as $\displaystyle x^{\frac{1}{m}} $. This is just the notation used. - Mar 13th 2010, 08:41 AMiwanttogotouni
Thanks!