# How to find logarithm of a number having negative characteristic.

#### rewt

Hi,
can anybody help me find logarithm of a number having negative characteristic?
For example, log(0.00462).
Any help would be highly appreciated.
Thanks.

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#### romsek

Math Team
$\log_{10}(10^k x) = \log(x) + k$

so for example I assume you can find $y=\log(4.62)$ where in this case $k=-3$

then

$\log(0.00462) = y - 3$

2 people

#### rewt

I don't understand \$ and euro currency sign. For which purpose they are used here, I don't understand your answer. Thanks for your reply. though. I can find all kinds of logs, but not logs having negative characteristics, e.g. log(0.00462) and log(.5143). It's easily found using a calculator, but I want to find it manually.
Any help would be highly appreciated.
Thanks.

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#### romsek

Math Team

Is that any better? Your browser isn't rendering the LaTex.

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2 people

#### rewt

Simply tell me how log(0.00462)=-2.3354 and log(.5143)=-.288791

#### mrtwhs

Simply tell me how log(0.00462)=-2.3354 and log(.5143)=-.288791
Just do what Romsek said.

Find log(4.62) and then subtract 3.

2 people

#### rewt

Now I understand. I have solved other problems like this. Thanks.

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