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5 December, 13:02

Without actually calculating the logarithm, determine what two integers the value of log (1.37*109) falls between.

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  1. 5 December, 13:37
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    First we need to find out what kind of logarithm rule is given, the given is logarithm product rule which states that a log of a product is equal to the sum of the log of the first base and the log of the second base.

    By:

    = log (1.37 x 10⁹) = log (1.37) + log (10⁹)

    = log (1.37) + 9

    = 9 + log (1.37)

    In the meantime, 1.37 is between 1 and 10 its logarithm will be between 0 and 1. Thus, the value of log (1.37 x 10⁹) falls between 9 and 10 because when you compose a scientific notation you will always have a number among 1 and 10 by 10 to some power. That power tells you the integer part of the logarithm.
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