Why we use log|x| ?what is meaning of log ? How this log is used in real world?

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How can I find log* of any number (say log 2 ) without using calculator, log table, or without memorising any log value of 2, 3, 5 etc.

* log x = log₁₀x

How we can find antilog( - 18.832 ) using log table

If $x < 0$ , $y < 0$ , then $l o g (x y)$ is equal to _______________ .

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