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

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

Thanks.

2. 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.
$\displaystyle x = log_2 \sqrt[8] 2$

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

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

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

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

$\displaystyle x = \frac{1}{8}$

3. 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.

4. Originally Posted by iwanttogotouni
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.

5. 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.

6. 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 $\displaystyle 1/2$ 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 $\displaystyle 2^{\frac{1}{2}}$ 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.

7. Thanks!