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Logarithms are used widely in science in chemistry, to calculate the pH of a solution. 
It is also used in photography, to determine density, curves etc.
It is used in astronomy, for the axes of their graphs and charts.
It is used in Richter scale for earthquakes and decibels related calculations.
Actually logs made many things possible. Before that, it was much tough for astronomers to work with huge numbers. Huge possibility of error was their during simple BODMAS. But with it, everything of such kind was reduced to simple calculations.

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For finding square root, Squares, cubes, any power, division and multiplications of large numbers.

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