Ahhhh so basically scientific calculators replaced them
Yes... you looked up the logs then added them up or took them away for amazing scientific answers like...
From memory... were log tables put together for artillery calculations or is that shite like...?
I have heard many tales as to why they might be useful but as I say have never had to use them.
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Logarithm functions, graphed for various bases: red is to base e, green is to base 10, and purple is to base 1.7. Each tick on the axes is one unit. Logarithms of all bases pass through the point (1, 0), because any number raised to the power 0 is 1, and through the points (b, 1) for base b, because a number raised to the power 1 is itself. The curves approach the y-axis but do not reach it because of the singularity at x = 0.
The 1797 Britannica explains logarithms as "a series of numbers in arithmetical progression, corresponding to others in geometrical progression; by means of which, arithmetical calculations can be made with much more ease and expedition than otherwise."
In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 103 = 1000, so log101000 = 3, and 25 = 32, so log232 = 5.
The logarithm of x to the base b is written logb(x) or, if the base is implicit, as log(x). So, for a number x, a base b and an exponent y,
\text{ if }x = b^y,\text{ then }y = \log_b (x)\,.
An important feature of logarithms is that they reduce multiplication to addition, by the formula:
\log (xy) = \log x + \log y \,.
That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers. The use of logarithms to facilitate complex calculations was a significant motivation in their original development.
Uses of logarithms
Logarithms are useful in solving equations in which exponents are unknown. They have simple derivatives, so they are often used in the solution of integrals. The logarithm is one of three closely related functions. In the equation bn = x, b can be determined with radicals, n with logarithms, and x with exponentials. See logarithmic identities for several rules governing the logarithm functions.
Science
Various quantities in science are expressed as logarithms of other quantities; see logarithmic scale for an explanation and a more complete list.
* In chemistry, the negative of the base-10 logarithm of the activity of hydronium ions (H3O+, the form H+ takes in water) is the measure known as pH. The activity of hydronium ions in neutral water is 10−7 mol/L at 25 °C, hence a pH of 7.
* The bel (symbol B) is a unit of measure which is the base-10 logarithm of ratios, such as power levels and voltage levels. It is mostly used in telecommunication, electronics, and acoustics. The Bel is named after telecommunications pioneer Alexander Graham Bell. The decibel (dB), equal to 0.1 bel, is more commonly used. The neper is a similar unit which uses the natural logarithm of a ratio.
* The Richter scale measures earthquake intensity on a base-10 logarithmic scale.
* In spectrometry and optics, the absorbance unit used to measure optical density is equivalent to −1 B.
* In astronomy, the apparent magnitude measures the brightness of stars logarithmically, since the eye also responds logarithmically to brightness.
* In psychophysics, the Weber–Fechner law proposes a logarithmic relationship between stimulus and sensation.
* In computer science, logarithms often appear in bounds for computational complexity. For example, to sort N items using comparison can require time proportional to the product N × log N. Similarly, base-2 logarithms are used to express the amount of storage space or memory required for a binary representation of a number—with k bits (each a 0 or a 1) one can represent 2k distinct values, so any natural number N can be represented in no more than (log2 N) + 1 bits.
* Similarly, in information theory logarithms are used as a measure of quantity of information. If a message recipient may expect any one of N possible messages with equal likelihood, then the amount of information conveyed by any one such message is quantified as log2 N bits.
* In geometry the logarithm is used to form the metric for the half-plane model of hyperbolic geometry.
* Many types of engineering and scientific data are typically graphed on log-log or semilog axes, in order to most clearly show the form of the data.
* In inferential statistics, the logarithm of the data in a dataset can be used for parametric statistical testing if the original data do not meet the assumption of normality.
* Musical intervals are measured logarithmically as semitones. The interval between two notes in semitones is the base-21/12 logarithm of the frequency ratio (or equivalently, 12 times the base-2 logarithm). Fractional semitones are used for non-equal temperaments. Especially to measure deviations from the equal tempered scale, intervals are also expressed in cents (hundredths of an equally-tempered semitone). The interval between two notes in cents is the base-21/1200 logarithm of the frequency ratio (or 1200 times the base-2 logarithm). In MIDI, notes are numbered on the semitone scale (logarithmic absolute nominal pitch with middle C at 60). For microtuning to other tuning systems, a logarithmic scale is defined filling in the ranges between the semitones of the equal tempered scale in a compatible way. This scale corresponds to the note numbers for whole semitones. (see microtuning in MIDI).
[edit] Exponential functions
One way of defining the exponential function ex, also written as exp(x), is as the inverse of the natural logarithm. It is positive for every real argument x.
The operation of "raising b to a power p" for positive arguments b and all real exponents p is defined by
b^p = \left( e^{\ln b} \right) ^p = e^{p \ln b }.\,
The antilogarithm function is another name for the inverse of the logarithmic function. It is written antilogb(n) and means the same as bn.
Which still makes no bloody sense to me at all ~ but note the reference to the Richter Scale. Useful if you happen to be in an earthquake and want to know how strong it is I suppose
Personally I'd be too busy running the other way.
