Logarithm inverse

Figure C2.8.7. Principal oxide growth rate laws for low- and high-temperature oxidation inverse logarithmic, linear, paralinear and parabolic.

Under certain conditions hydrogen cyanide can polymerize to black soHd compounds, eg, hydrogen cyanide homopolymer [26746-21-4] (1) and hydrogen cyanide tetramer [27027-02-2], C H N (2). There is usually an incubation period before rapid onset of polymer formation. Temperature has an inverse logarithmic effect on the incubation time. Acid stabilizers such as sulfuric and phosphoric acids prevent polymerization. The presence of water reduces the incubation period. 

The oxidation of aluminium at room temperature is reported to conform to an inverse logarithmic equation for growth periods up to 5 years duration. At elevated temperatures, oxidation studies over shorter periods illustrate conformity to parabolic, linear and logarithmic relationships according to time and temperature. These kinetic variations are attributed to different mechanisms of film formation . ... 

The numbers whose natural logarithms are 4.606 and —6.908 are 100 and 0.001, respectively. Notice that if the inverse logarithm is positive, the corresponding number is larger than 1 if it is negative, the number is smaller than 1. 

The method used to find inverse logarithms depends on the type of calculator. On certain calculators, you enter the number and then press, in succession, the [ihv] and either [log] or [lux] keys. With other calculators, you press the [ io ) or key. Either way, you should find that... 

In taking the inverse logarithm of a number, retain as many significant figures as there are after the decimal point in the number. Thus... 

The rules for significant figures involving natural logarithms and inverse logarithms are somewhat more complex than those for base-10 logs. However, for simplicity we will assume that the rules listed above apply here as well. Thus... 

Significant figure A meaningful digit in a measured quantity, 9,20-2 lq ambiguity in, 10 in inverse logarithms, 645-647 in logarithms, 645-647 Silicate lattices, 243 Silicon, 242-243 Silver, 540-541 Silver chloride, 433,443-444 Simple cubic cell (SC) A unit cell in which there are atoms at each comer of a cube, 246... 

A note on good practice Exponential functions (inverse logarithms, e ) are very sensitive to the value of x, so carry out all the arithmetic in one step to avoid rounding errors. 

An inverse logarithmic scale was also constructed along the horizontal... 

If the template is used as an inverse logarithmic scale, and is set at a given value of Z—Ss on the inverse scale of the graph, then values of D on the... 

Fig. 5.10. Plot of the inverse logarithm of the self-diffusion constant of BPA-PC, for a length N = 20 of the coarse-grained chains, vs. temperature. Straight line indicates the Vogel-Fulcher [187] fit. From [28]...

The oxidation of iron by (dry) air at ambient temperature proceeds according to the inverse logarithmic rate law, which may be written... 

Since not all electronic calculators are alike, detailed instructions cannot be given here. Read your instruction manual. You should purchase a calculator which, in addition to , —, x, and a functions, provides at least the following scientific notation (powers of ten) logarithms and antilogarithins (inverse logarithms) both natural and common (base ten) and exponentials (y ). If it has these functions, it will probably have reciprocals (1/jt), squares, square roots, and trigonometric functions as well. 

When a common log is given, to find the number it represents, we must carry out the process of exponentiation. For example, if the log is 2.673, then N = 102 673. The process of exponentiation is also called taking the antilog, or the inverse logarithm, and is easily carried out by using a calculator. 

The inverse (logarithmic scale) distribution of the Cole-Davidson type yields... 

Moist-heat sterilization is achieved when water vapor (or, more generically, moist heat, i.e., a suitable combination of temperature and humidity) at a definite temperature is introduced or generated (even indirectly) at the level of the micro-organisms to be inactivated and is maintained in such conditions for a definite time. As explained in detail hereafter, moist-heat sterilization proceeds as an inverse logarithmic progression. Therefore, only a treatment of infinite duration provides absolute certainty that all micro-organisms have been inactivated. 

Equation 1.4 directly implies the time behavior (rate) of oxide growth. An inverse logarithmic growth law according to the following expression can be derived to a good approximation (Cabrera and Mott [55]) ... 

Taking the inverse logarithm (antUog) of both sides of the equation gives... 

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