# Calculate log 3.25 x 10^-3 . The answer is -2.4881 although, according to my calculation the answer is -3.5119

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Expert Answers

durbanville | Certified Educator

Logs and exponents are the inverse functions of each other.

`log 3.25 times 10^(-3)` indicates that both terms have the same base (10). Remember that when a log does not indicate a base (which would be the subset between "log" and , in this case, 10,), it is always base 10.

Now convert the exponent into a decimal fraction in keeping with the other term. We know that

`10^-3= 1/ 10^3= 1/1000= 0.001`

Next convert this into a log using the rules:

`= log(10) 0.001`

We now have:

`log 3.25times log 0.001` .

We do not need to indicate the base as it is 10 which we previously established.

This can be written as

`log (3.25 times 0.001) = -2.4881` OR in terms of the rules of logs where

`log(m timesn) = log m + log n`

`log 3.25 + log 0.001 = -2.4881`

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