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

  • Thread starter zak100
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In summary: 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
  • #1
zak100
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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.
 
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  • #2
zak100 said:
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?
zak100 said:
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##.
 
  • #3
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.
 
  • #4
What makes you think that the log of 36 to the base 2 is 18? It's not.
 
  • #5
zak100 said:
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)##
 
  • #6
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.
 
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  • #7
The log of a product of two factors is equal to the sum of the logs if the factors.
 
  • #8
zak100 said:
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.
 
  • #9
Thanks all of you. This problem is solved now.

Zulfi.
 
  • #10
Okay, equation is:
##t_{comm} = \mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1) ##
 

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

1. What is a log base 2 equation?

A log base 2 equation is an equation in the form of log2(x) = y, where x is the input value and y is the output value. It represents the power to which 2 must be raised to equal the input value.

2. How do I solve a log base 2 equation?

To solve a log base 2 equation, you can use the inverse property of logarithms. This means that if log2(x) = y, then 2y = x. You can also use logarithm rules such as the product rule and quotient rule to simplify the equation.

3. What is the importance of solving a log base 2 equation?

Solving a log base 2 equation is important in many fields of science, such as computer science, physics, and engineering. It allows us to solve complex equations involving exponential growth and decay, and helps us understand the relationship between different variables.

4. What are some common mistakes when solving a log base 2 equation?

One common mistake is forgetting to apply the inverse property of logarithms, resulting in an incorrect solution. Another mistake is not simplifying the equation using logarithm rules, which can make the equation more difficult to solve.

5. Are there any tips for solving a log base 2 equation?

One tip is to always check your solution by plugging it back into the original equation. Another tip is to practice using logarithm rules to simplify the equation before attempting to solve it. Also, make sure to pay attention to any restrictions on the domain of the equation, as logarithms cannot be negative or equal to 0.

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