(–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) [ log2 5 - 3] =
-3 [ -3/8 -5/8] - [ (3/8) log2 3 + (5/8) log2 5 ] =
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]
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)) =
(−38Log2(38))+(−58Log2(58))=−18[3Log2(38)+5Log2(58)]=−18[Log2(38)3+Log2(58)5]=−18[Log2((38)3∗(58)5)]=−18[Log2((33∗55)88)]=−18[Log2(33∗55)−Log288]=−18[Log2(27∗3125)−8Log28]=−18[Log2(84375)−8Log223]=−18[Log2(84375)−24Log22]=−18[Log2(84375)−24]=3−[Log2(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
3−log2(84375)8=0.9544340029249647
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
3−(log10(84375)log10(2))8=0.9544340029249649
(–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) [ log2 5 - 3] =
-3 [ -3/8 -5/8] - [ (3/8) log2 3 + (5/8) log2 5 ] =
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]