+0  
 
0
1
1223
2
avatar

(–3/8 Log2(3/8)) + (– 5/8 Log2(5/8)) =

 
 
 
 Apr 5, 2015

Best Answer 

 #2
avatar+94619 
+10

(–3/8 Log2(3/8)) + (– 5/8 Log2(5/8))=

(-3/8) [log2 3 - log2 8] + (-5/8) [log2 5 - log2  8] =

(-3/8) [log2 3  - 3] + (-5/8) [ log5  - 3] =

-3 [ -3/8 -5/8]  - [ (3/8) log2 3 + (5/8)  log5 ] =

3  - [ 1/8)] * [ 3 log2 3 + 5 log2 5 ]  =

3 - [1/8] * [ log2 3^3 +  log2 5^5] =

3 - [1/8] * [ log2 27 + log2 3125] =

3 - [1/8] * [log2 (27 * 3125)] =

3 - [log2 84375] / 8 =

[24 -  log2 84375 ] / 8 =  

 [about  0.954434]

 

  

 Apr 5, 2015
 #1
avatar+95375 
+10

This answer has been modified, 

Thanks CPhill and Alan for letting me know of my careless error :))

 

(–3/8 Log2(3/8)) + (– 5/8 Log2(5/8)) =

 

$$\\(-\frac{3}{8}Log_2(\frac{3}{8})) + (-\frac{5}{8} Log_2(\frac{5}{8})) \\\\
=-\frac{1}{8}[3Log_2(\frac{3}{8}) + 5 Log_2(\frac{5}{8})] \\\\
=-\frac{1}{8}[Log_2(\frac{3}{8})^3 + Log_2(\frac{5}{8})^5] \\\\
=-\frac{1}{8}[Log_2((\frac{3}{8})^3*(\frac{5}{8})^5 )] \\\\
=-\frac{1}{8}[Log_2(\frac{(3^3*5^5)}{8^8})] \\\\
=-\frac{1}{8}[Log_2 (3^3*5^5)-Log_2 8^8] \\\\
=-\frac{1}{8}[Log_2 (27*3125)-8Log_2 8] \\\\
=-\frac{1}{8}[Log_2 (84375)-8Log_2 2^3]\\\\
=-\frac{1}{8}[Log_2 (84375)-24Log_2 2]\\\\
=-\frac{1}{8}[Log_2 (84375)-24]\\\\
=3-\frac{[Log_2 (84375)]}{8}\\\\$$

 

This is the same as Chris's answer below.  :)

The question is finished but if you want an approximation ...

 this can be entered into the web 2 calc like this

3-log(84375,2)/8

 

$${\mathtt{3}}{\mathtt{\,-\,}}{\frac{{{log}}_{{\mathtt{2}}}{\left({\mathtt{84\,375}}\right)}}{{\mathtt{8}}}} = {\mathtt{0.954\: \!434\: \!002\: \!924\: \!964\: \!7}}$$

 

Most calcs only do base 10 or base e so this is how you would do it on one of those (uaing change of base rule)

 

3-(log(84375)/log(2))/8

 

$${\mathtt{3}}{\mathtt{\,-\,}}{\frac{\left({\frac{{log}_{10}\left({\mathtt{84\,375}}\right)}{{log}_{10}\left({\mathtt{2}}\right)}}\right)}{{\mathtt{8}}}} = {\mathtt{0.954\: \!434\: \!002\: \!924\: \!964\: \!9}}$$

.
 Apr 5, 2015
 #2
avatar+94619 
+10
Best Answer

(–3/8 Log2(3/8)) + (– 5/8 Log2(5/8))=

(-3/8) [log2 3 - log2 8] + (-5/8) [log2 5 - log2  8] =

(-3/8) [log2 3  - 3] + (-5/8) [ log5  - 3] =

-3 [ -3/8 -5/8]  - [ (3/8) log2 3 + (5/8)  log5 ] =

3  - [ 1/8)] * [ 3 log2 3 + 5 log2 5 ]  =

3 - [1/8] * [ log2 3^3 +  log2 5^5] =

3 - [1/8] * [ log2 27 + log2 3125] =

3 - [1/8] * [log2 (27 * 3125)] =

3 - [log2 84375] / 8 =

[24 -  log2 84375 ] / 8 =  

 [about  0.954434]

 

  

CPhill Apr 5, 2015

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.