when finding the logarithm of a product, am I adding exponential values, providing a formula as a solution like base exp+base exp, combining exponents so that if my values were 10 to the third + 5 to the sixth I would have 15 to the ninth or 10 to the third and ten to the third would equal 10 to the sixth or 20 to the sixth? am i even supposed to add the exponents whatsoever.
this is what i know: the logarithm of a product is the sum of the factors.
logarithm of base (n)=(x)+log of base (n)=(x)
it was actually a generalized question. i wasn't looking for advice on a specific problem so it's as specific as it can be. when finding a logarithm, i'm confused as to whether to add the exponents like any other values?
i actually didn't really get along very well at all in mathematics, and was looking up math terms on wikipedia. that encyclopaedia can get really wordy though, so i was unsure of what is was saying, in regard to the final enumeration. i guess i understood what was said in plain terms, but it doesn't look as if it's accuracy would be applicable across generalized mathematics to me, so that log(xy)=log(x)+log(y) may or may not require a more proportionate evaluation of exponential values. for instance, 1000=10 to the third. presenting that twice for simplicity is straight forward enough and the common formulation is as well (as I understood it) so that the logarithm of 10 to the third + ten to the third is twenty to the 6th. Although it seemed to me that across mathematical applications like physiological or other chemical maths, acoustics, or physics that the absolute or floor value (if you want to present it philosophically) could look the same and be two entirely different mathematical numbers. As stated I'm beginning mathematics and I can only apply what I've learned of linguistics (which you might have heard it said that numbers and letters don't belong together, it gets too complicated). The end result of my newdom :/ is that I can't present a complex theoretical formula, but moreso was just wondering if the logic I'm applying is feasible if I wanted or happened upon a logarithmic use when examining physical happenstance versus numeric calculation for expressive purposes or absented new computer cgi, algorithmic purposes.
@mr fantastic: is that doogie howser? o.o
and i apologize for not being more attentive to the board, the internet services here were unavailable for some time. thanks for the replies, and i apologize for not having a less controversial or long winded question.