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Logarithms

Suppose you have an equation, a=bc.
Then we say, c=logb of a, or, c=logb(a).
For instance, 1000=103. Then,
3=log10(1000).

To calculate this, run windows calculator (click on the start menu, click on "run," type "calc" into the search field and press enter. Set the calculator to "scientific" by clicking on the "view" menu at the top of the calculator window and clicking on the "scientific" option.

Look for the "log" button (it's a purple key in the middle of the third purple row). If you type in a number and press this button, you'll get the base 10 log (that is, log10) of whatever number you enter.

Now, suppose you expect Coca-Cola to be able to grow it's volume by 70% over the long term, and expect volume to grow at 4% per year. How long will it take to achieve this 70% growth? You want to find x for the equation: 1.7=1.04x.
So x=log1.04 of 1.7.
In order to calculate this, we'll need to use the following property:

loga(x)
----------=logy(x)
loga(y)

For this problem, we'd say that

log10(1.7)
----------=log1.04(1.7)=13.529
log10(1.04)

so assuming our numbers are correct, Coca-Cola will be able to main its volume growth for about 13 and a half years.