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.
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.
(It/I0) x 100
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