Logarithmic function 27/35 Functions Mathematics Onlineschool.cz
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Logarithmic functions are functions that have an independent variable x in the argument of the logarithm. The logarithmic function is the inverse of the exponential function and is therefore connected by symmetry along the 1st and 3rd quadrant axes. The basic form looks like y=log_a(x) If you need to practice more with functions (linear, quadratic, with square root, exponential, logarithmic, with absolute value) along with their graphs and shifts, you can find a collection of solved examples at ???????????????????????? https://onlineschool.cz/videosbirky/f... The base of the logarithm a must be a number from the interval (0;1)∪(1;∞). The number x is always positive by definition of the logarithm, therefore the domain of definition is the interval (0;∞). The shape of the graph of a logarithmic function The base of the logarithm determines the shape of the function, because bases greater than 1 are increasing functions, and less than 1 are decreasing. Due to the restriction of the domain of definition, the graph of a logarithmic function has an asymptote x=0. It approaches this line, but never intersects it. No matter what base a logarithmic function has, all these functions pass through the point [1;0]. This is because every base (positive number except one) to zero is equal to one. Properties of the logarithmic function Logarithmic functions are simple, non-periodic, unbounded, neither even nor odd, and their base determines whether the function is decreasing or increasing. Logarithmic scales One of the common uses of logarithms is logarithmic scales (or scales). These are scales whose measure is the logarithm of a certain quantity, not the quantity itself. In other words, the values on such a scale are exponents of a certain base. This allows us to describe quantities with a large dispersion over a relatively small section. If we had a scale with a base of ten, the value 1 would mean 10^1, the value 6 would mean 10^6. On 6 scale divisions, we have described quantities with a range of one million. Logarithmic scales measure, for example, the intensity of an earthquake (Richter scale), the loudness of sound (decibels), the acidity or alkalinity of solutions (pH scale). The entire video is available under the Attribution-ShareAlike 3.0 Unported license according to https://creativecommons.org/licenses/... Created with GeoGebra software - www.geogebra.org You can also find this video on the Onlineschool.cz website at https://onlineschool.cz/matematika/lo... Subscribe so you don't miss any new videos! https://www.youtube.com/c/onlineschoo... You can follow my work on Facebook: / onlineschoolcz You can find all videos from mathematics and other technical subjects at https://onlineschool.cz
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