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So, I found this method, I don't think I was the first to, though, but I don't see any post related to this anywhere on the internet, so maybe there's a slim chance I was the first? Anyway, it doesn't really matter. The method does not give the precise result, only approximations, but I find it really useful, since when I have to use logarithms, I only work with approximations. Here it is:

Log(a+b) = Log(2) + Log(SQRT)(a*b)

It works with any base you choose, as long as it is the base for Log(a+b), Log(2) and Log(SQRT)(a*b) at the same time

See the "equals to" symbol as an "is approximate to" symbol

Also, "(SQRT)" means "square root of", quite obvious

And since Log(SQRT)(a*b) is (Log(a*b))/2, then

Log(a+b) = Log(2) + (Log(a*b))/2

And since (Log(a*b))/2 = (Log(a) + Log(b))/2, then

Log(a+b) = Log(2) + (Log(a) + Log(b))/2

In base 10, Log(2) is approximately 0,3, so

Log(a+b) = 0,3 + Log(SQRT)(a*b) in base 10

***IMPORTANT***

The bigger (a+b) is, the closer the results will be to the real values

If a>b

The smaller (a-b) is, the closer the results will be to the value

If b>a

The smaller (b-a) is, the closer the results will be to the value.

Example:

If you use this to find Log(11) and you want to use only natural numbers, you should use "6" and "5" for "a" and "b", it will not work if you use, instead, "10" and "1" for "a" and "b"

Also, "a" and "b" can be any REAL number to make this work, I don't know if this works with complex numbers, but I'm guessing it doesn't.

Anyway, I hope this helps you guys, any questions just ask me :)

Log(a+b) = Log(2) + Log(SQRT)(a*b)

It works with any base you choose, as long as it is the base for Log(a+b), Log(2) and Log(SQRT)(a*b) at the same time

See the "equals to" symbol as an "is approximate to" symbol

Also, "(SQRT)" means "square root of", quite obvious

And since Log(SQRT)(a*b) is (Log(a*b))/2, then

Log(a+b) = Log(2) + (Log(a*b))/2

And since (Log(a*b))/2 = (Log(a) + Log(b))/2, then

Log(a+b) = Log(2) + (Log(a) + Log(b))/2

In base 10, Log(2) is approximately 0,3, so

Log(a+b) = 0,3 + Log(SQRT)(a*b) in base 10

***IMPORTANT***

The bigger (a+b) is, the closer the results will be to the real values

If a>b

The smaller (a-b) is, the closer the results will be to the value

If b>a

The smaller (b-a) is, the closer the results will be to the value.

Example:

If you use this to find Log(11) and you want to use only natural numbers, you should use "6" and "5" for "a" and "b", it will not work if you use, instead, "10" and "1" for "a" and "b"

Also, "a" and "b" can be any REAL number to make this work, I don't know if this works with complex numbers, but I'm guessing it doesn't.

Anyway, I hope this helps you guys, any questions just ask me :)

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