What is the optimal communication time for a given set of parameters?

[zak100]

Homework Statement

I can't solve a log base 2 equation

Relevant Equations

$\mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$

Hi,
I am trying to solve the following equation:
$\mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$
$\mathbf (10+0.01 * 1000) log(36) + 2 * 2(5)$

I think log(36) would be 18. Note log is $\mathbf log_2$

Somebody please guide me.

Zulfi.

 

[Mark44]

Hi,
I am trying to solve the following equation:
$\mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$
$\mathbf (10+0.01 * 1000) log(36) + 2 * 2(5)$

Neither of these is an equation. Are you trying to simplify this expression?

I think log(36) would be 18. Note log is $\mathbf log_2$

No.
If it were true that $\log_2(36) = 18$, then it would also have to be true that $2^{18} = 36$. $\log_2(36)$ is somewhere between 5 and 6, because $32 = 2^5 < 36 < 2^6 = 64$.

Also, there are conversion formulas for changing a log in one base to a log in a different base. Most calculators don't have buttons for $\log_2$, but they do have them for $\log_{10}$ and $\log_e = \ln$.

 

[zak100]

Hi,
Okay, equation is:
$t_{comm} = \mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$
I am able to find out how to calculate $log_2$

Zulfi.

 

[Chestermiller]

What makes you think that the log of 36 to the base 2 is 18? It's not.

 

[Mark44]

Hi,
Okay, equation is:
$t_{comm} = \mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$
I am able to find out how to calculate $log_2$\

Zulfi.

Here's how to convert from one log base to another, assuming you want to write $\log_a(x)$ in some other base, b.
Let $y = \log_a(x)$
$\Leftrightarrow a^y = x$
$\Leftrightarrow \log_b(a^y) = \log_b(x)$
$\Leftrightarrow y\log_b(a) = \log_b(x)$
$\Leftrightarrow y = \frac{\log_b(x)}{\log_b(a)}$
$\Leftrightarrow \log_a(x) = \frac{\log_b(x)}{\log_b(a)}$
In the last equation, I replaced y with $\log_a(x)$

 

[zak100]

Hi,
I tried this :
$log_2 2^2 * 9$

2 goes with 2 so we are left with 2 * 9 which is 18. I did something like that in my Algorithm course.

Thanks for asking.

Zulfi.

 

[Chestermiller]

The log of a product of two factors is equal to the sum of the logs if the factors.

 

[Mark44]

Hi,
I tried this :
$log_2 2^2 * 9$

2 goes with 2 so we are left with 2 * 9 which is 18. I did something like that in my Algorithm course.

Is the above $\log_2(2^2) * 9$ or is it $\log_2(2^2 * 9)$?
Without parentheses, what you wrote is ambiguous.

Also, what you have above doesn't seem related to what you were asking about:

$\mathbf (10+0.01 * 1000) log(36) + 2 * 2(5)$

It seems that you are still trying to figure out how to calculate $\log_2(36)$

Simplifying your expression above, it is $10010\log_2(36) + 20$. I don't see what this has to do with what I quoted at the top of this post.

 

[zak100]

Thanks all of you. This problem is solved now.

Zulfi.

 

[zak100]

Okay, equation is:
$t_{comm} = \mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1)$