How to find logarithms easily How to find the value of log2.7 by any shortcut or alternative methods?

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Notice that you may write 2.7=27/10, hence log 2.7 = log (27/10)

You need to remember the quotient property of logarithms, thus you should conver the logarithm log (27/10) in a difference of two logarithms such that:

log (27/10) = log 27 - log 10

You need to remember that log 10 = 1, hence log (27/10) = log 27 - 1

You may write 27 = 3^3 => log 27 = log 3^3 => log 27 = 3*log 3

You may use tables of common logarithms (base 10) for 1 to 10 to find log 3 = 0.477.

log 2.7 = 3*0.477 - 1 = 0.431

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I am not sure if you are only looking for methods to calculate the logarithms by hand, but there are also several online calculators. Even if you are learning how to find logarithms by hand, you can use an online calculator to check your work. Here's one I found easily, but there are more. http://www.1728.org/logrithm.htm
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It depends on the number you are taking the log of. If you have a number, such as 1 x 10^-3, then the log will be -3. If the number increases (ie 2 x 10^-3), the value of the log will increase to -2.7. Knowing this allows us to estimate the value to either make a reasonable estimate of the answer or to evaluate if an answer is in the appropriate range.
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