Question 1100090: I'm still trying to figure out exactly how logarithms work...and I don't quite understand the way my math book explains it. Anyhow, I have this problem: "Use a calculator to write 0.000715*10^-4 as an exponential expression whose base is 10. Then use logarithm notation to make the same statement." I would be really grateful if someone would explain to me the hows and whys of solving this problem. Thank you!
Answer by josgarithmetic(39623)   (Show Source):
You can put this solution on YOUR website! A logarithm is an exponent, and logarithms follow rules of exponents.
b, the base
x, the exponent, and later, called logarithm
y, result of raising base b, to power x.
Different notation:
Not a very thorough explanation, but maybe your book will make more sense for you.
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The specific numerical example you asked about:
which you wanted completely as base of 10, raised to some power.
Using scientific notation, given numerical expression is
but you want ALL of the number as 10 raised to some power.
You use either table of logs or a calculator to find what is  .
The base is 10;
the logarithm is n;
the antilog is 7.15.
 . Do whatever you need on your calculator to find this n. Mine (on the computer) indicates  ;
If using Google, this tells me log(10,7.15)=0.854306;
(You probably want to near more than as 0.8543.)
So now your entire given number is  .
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