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A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a ...
Decibel. The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel ( B ). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 10 1/10 (approximately 1.26) or root-power ratio of 10 1/20 (approximately 1.12 ).
Log-normal distribution. In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution.
The logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks: where x ( t) is the overshoot (amplitude - final value) at time t and x(t + nT) is the overshoot of the peak n periods away, where n is any integer number of successive, positive peaks. The damping ratio is then found from the ...
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Common logarithm. A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ...
ln (r) is the standard natural logarithm of the real number r. Arg (z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg (x + iy) = atan2 (y, x). Log (z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
The Mote and the Beam is a parable of Jesus given in the Sermon on the Mount [1] in the Gospel of Matthew, chapter 7, verses 1 to 5. The discourse is fairly brief, and begins by warning his followers of the dangers of judging others, stating that they too would be judged by the same standard. The Sermon on the Plain has a similar passage in ...