Difference between revisions of "Math for CS Review"

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(Memorize)
(Memorize)
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* ''Logarithms''
 
* ''Logarithms''
 
** log<sub>b</sub>x = y, means b<sup>y</sup> = x, for any b > 1
 
** log<sub>b</sub>x = y, means b<sup>y</sup> = x, for any b > 1
 +
** log<sub>10</sub>1000 = 3
 +
** log<sub>2</sub>1024 = 10
 
** log<sub>b</sub>x = log<sub>c</sub>x / log<sub>c</sub>b, for any b > 1, c > 1
 
** log<sub>b</sub>x = log<sub>c</sub>x / log<sub>c</sub>b, for any b > 1, c > 1
 
** log<sub>2</sub>10 is about 3.32
 
** log<sub>2</sub>10 is about 3.32
 
** log<sub>b</sub>(xy) = y log<sub>b</sub> x, for any b > 1
 
** log<sub>b</sub>(xy) = y log<sub>b</sub> x, for any b > 1

Revision as of 19:01, 6 January 2020

Memorize

These are things you need to memorize.

  • Order of operations: first parenthesis, then exponents, then multiplication/division/modulus, then addition and subtraction. And left to right.
  • Powers/exponents
    • 210 = 1024, roughly 1 thousand
    • 2a+b = 2a * 2b
    • ya+b = ya * yb
    • 2-a = 1 / (2a)
    • 220 = 1024 × 1024, roughly 1 million
    • 230 = 1024 × 1024 × 1024, roughly 1 billion
  • Logarithms
    • logbx = y, means by = x, for any b > 1
    • log101000 = 3
    • log21024 = 10
    • logbx = logcx / logcb, for any b > 1, c > 1
    • log210 is about 3.32
    • logb(xy) = y logb x, for any b > 1