• Mar 12th 2010, 08:47 PM
iwanttogotouni
Sorry, I couldn't paste properly from Word. So I want to Print Screen it.

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

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

Thanks.
• Mar 12th 2010, 09:04 PM
Gusbob
Quote:

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

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 $log_a (a) = 1$

$x = \frac{1}{8}$
• Mar 12th 2010, 09:08 PM
iwanttogotouni
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, 09:16 PM
iwanttogotouni
• Mar 12th 2010, 09:24 PM
Gusbob
Quote:

Originally Posted by iwanttogotouni

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.
• Mar 12th 2010, 09:25 PM
iwanttogotouni
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.
• Mar 13th 2010, 02:36 AM
Gusbob
Quote:

Originally Posted by iwanttogotouni
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.
• Mar 13th 2010, 09:41 AM
iwanttogotouni
Thanks!