T.O. 33B-1-1 6-27 For  example,  an  increase  in  the  amount  of  blackening  from  one  area  of  a  particular  film  to  another  that reduces the proportion of the incident light transmitted from 50 to 25 percent would cause the film density to change from 0.3 to 0.6. 6.4.1.4.1 Table 6-6 shows more examples of typical relationships between light transmission and density.  A typical density used in practical radiography is 2.0 and represents one- percent transmittance. Table 6-6.  Relationship of Light-Transmission to Film Density. Transmittance (I_t/I₀₎ Percent Transmittance (I_t/I₀) x 100 Opacity (I₀/I_t) Film Density Log₁₀ (I₀/I_t) 1.00 0.50 0.25 0.10 0.01 0.001 0.0001 100 50 25 10 1 0.1 0.01 1 2 4 10 100 1,000 10,000 0 0.3 0.6 1.0 2.0 3.0 4.0 6.4.1.5 Logarithms for Density and Exposure Calculations. Logarithms  are  used  extensively  in  X-ray  exposure  calculations  and  in  the  measurement  of  X-ray  film  density. Therefore,  it  is  required  that  radiographers  be  sufficiently  familiar  with  logarithms  so  that  they  can  perform  some simple calculations.  A brief review of logarithms and their use is therefore included here.  More detail can be found in various  handbooks  and  intermediate  mathematics  texts.    Logarithms  are  used  because  they  provide  a  convenient method of handling very large ranges of numbers, and they reduce calculations involving multiplication and division to addition  and  subtraction.    The  logarithm  is  the  power  (or  exponent)  to  which  the  base  must  be  raised  to  give  the original  number.    Logarithms  may  be  taken  from  any  base;  however,  most  calculations  in  radiography  involve  either the base 10 or the base e (2.718).  Logarithms to the base 10 are indicated by "log x," and logarithms to the base e are denoted  by  "ln  x."    For  the  moment,  let  us  consider  logarithms  to  the  base  10:  log  100  =  2,  because  10²  =  100. Similarly,  the  logarithm  of  1,000  is  3  or:  log  1,000  =  3,  since  10³  =  1,000.    The  logarithms  of  all  numbers  that  are integer  powers  of  10  (i.e.,  10,  100,  1,000,  etc.)  are  whole  numbers  (1,  2,3,  etc.).    Logarithms  of  other  numbers  are decimal numbers and are found in tables of logarithms or calculated on some hand calculators.  A table of four-place logarithms  to  the  base  10  is  given  in  Table  6-8.    The  logarithm  is  made  up  of  two  basic  parts,  the  "characteristic", which  is  the  number  before  the  decimal  point  and  the  "mantissa",  which  is  the  number  after  the  decimal  point.   The characteristic   indicates   the   order   of   magnitude   of   the   number   x;   for   example,   numbers   10   through   99   have   a characteristic of 1.  Characteristics for other ranges are given in Table 6-7.  The mantissa is determined by the digits of the number.  In Table 6-8, the mantissa of 328, for example, is found by going to the number 32 along the left hand side and looking across that row under the column marked "8." We see in the table that the mantissa of 328 is given as 5159.    What  is  the  logarithm  of  328?    From  Table  6-7,  it  can  be  seen  that  the  characteristic  of  328  would  be  2. Therefore, log 328 is equal to 2.5159. Table 6-7.  Characteristics of Logarithms Number Characteristic 1 10 100 1,000 10,000 0 1 2 3 4