An explanation of this is that although the logarithm of the lognormal density function is quadratic in, yielding a " bowed " shape in a log-log plot, if the quadratic term is small relative to the linear term then the result can appear almost linear.

( This notation gives the logarithm of the iron-to-hydrogen ratio relative to the Sun.

This value gives the logarithm of the abundance relative to the Sun ; the actual proportion is 3. 2 – 4. 6 % of the solar abundance.

This quantity is normally listed as the base – 10 logarithm of the proportion relative to the Sun ; for NGC 6809 the metallicity is given by: = – 1. 94 dex.

If is a primitive element of a finite field, then the Zech logarithm relative to the base is defined by the equation

The logarithm of this ratio is – 0. 20, indicating that the proportion of iron is about 10 < sup >– 0. 20 </ sup >, or 63 % of the Sun.

This is expressed by the logarithm of the ratio of iron to hydrogen, compared to the same proportion in the Sun.

For other stars, the metallicity is often expressed as "", which represents the logarithm of the ratio of a star's iron abundance compared to that of the Sun ( iron is not the most abundant heavy element, but it is among the easiest to measure with spectral data in the visible spectrum ).

For example, the notation "" represents the difference in the logarithm of the star's oxygen abundance compared to that of the Sun and the logarithm of the star's iron abundance compared to the Sun:

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

Since pH is defined as the negative logarithm of the concentration of hydronium ions, acids thus have pHs of less than 7.

For instance, binary search is said to run in a number of steps proportional to the logarithm of the length of the list being searched, or in O ( log ( n )), colloquially " in logarithmic time ".

The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.

The work factor for breaking Diffie-Hellman is based on the discrete logarithm problem, which is related to the integer factorization problem on which RSA's strength is based.

The extinction or absorbance of the radiation is the logarithm ( decadic or, more usually, natural ) of the reciprocal of the transmittance:

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians.

We now know that the above equation is true modulo integer multiples of, but Cotes missed the fact that a complex logarithm can have infinitely many values due to the periodicity of the trigonometric functions.

The logarithm of a complex number is thus a multi-valued function, because is multi-valued.

For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.

Elliptic curve cryptography is vulnerable to a modified Shor's algorithm for solving the discrete logarithm problem on elliptic curves.

This example assumes that the natural logarithm of a person's wage is a linear function of ( among other things ) the number of years of education that person has acquired.

* is a logarithm, that is, ∂ u =

Use of mantissa in place of significand or coefficient is discouraged, as the mantissa is traditionally defined as the fractional part of a logarithm, while the characteristic is the integer part.

The value distribution is similar to floating-point, but the value-to-representation curve, i. e. the graph of the logarithm function, is smooth ( except at 0 ).

This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or compared to a critical value to decide whether to reject the null model in favour of the alternative model.

for the multiplicative structure on O < sup >∗</ sup >, can be compared with the cohomology group H < sup > 1 </ sup >( M, O ) with its additive structure by taking a logarithm.

Since E < sub > m </ sub > is small compared to E *, a Taylor series expansion can be performed on the latter logarithm around the energy E *.

The, or logarithm of the star's surface gravity, is about 4. 4 — very close to the for the Sun.

The logarithm is based on powers of ten ; stars with a value of + 1 have ten times the metallicity of the Sun ( 10 < sup > 1 </ sup >).

The results of the study, based on collision integrals computed from the latest critically evaluated data on intermolecular forces in air, will be reported in the form of a table of viscosity, thermal conductivity, thermal diffusion, and diffusion coefficients at temperatures of 1,000 to 10,000 Af and of logarithm of pressure in atmospheres from Af to Af times normal density.

The frequency axis of this symbolic diagram can be linear or logarithm ically scaled.

For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform.

25 ° C ) and R = 8. 3145 J /( K · mol ), the equation above can be expressed on base — 10 logarithm as shown below:

( where " ln " means natural logarithm, i. e. log with base e ).

Now, taking this derived formula, we can use Euler's formula to define the logarithm of a complex number.

and in fact this can be used as the definition for the complex logarithm.

This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system ( microstates ) which could give rise to the observed macroscopic state ( macrostate ) of the system.

Neither the natural logarithm nor the square root functions can be continued analytically to an entire function.

By starting with the field of rational functions, two special types of transcendental extensions ( the logarithm and the exponential ) can be added to the field building a tower containing elementary functions.

This terminology comes from the manner in which logarithm tables were used before computers became commonplace.

* Logarithmic number systems represent a real number by the logarithm of its absolute value and a sign bit.