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.
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.
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.
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.