I DO NOT understand logarithms?

Question

Can someone explain them to me in English? My textbook is confusing. I'm Honors Alg 2 level, so just the basic ones.

Answer 1

You know how square rooting takes a number and changes it into a different number? Square rooting 4 changes it into 2. Square rooting 256 changes it into 16. Things that you can do, which take a number and change it into another number are called functions.

Logs are just another kind of function. You take the log of a number, it changes it into a different number. The textbooks will say, "it maps numbers from the domain onto numbers in the range" or something like that. It's just that with logs, it's just a little harder to understand exactly what it's doing to the given number. Taking the log of 21 says, "what number must I raise 10 to in order to get 21?" (in numbers, 10^x = 21?)

Why does anyone want to map numbers like that, using logarithms? Because of the properties that you've seen and others have listed. These properties turn out to be very useful, because among other things, they "undo" exponentials. If you have something up in the exponent that you want to solve for, you can (must) use logs to get at them. You need them to solve a problem like:

3^x = 12 ; find x

you must take the log of both sides, then use the laws of logs to solve for x:

log(3^x) = log 12
x(log 3) = log 12
x = (log 12)/log 3)

no other way to do that problem, except by logs.

Answer 2

An example: log ( base 10 ) 1000 = 3 because 10³ = 1000.

Logarithms are the "opposite" so to speak of exponents. Take any number and express it as b raised to the power x. Then log ( base b ) of that number is x.

Answer 3

Theory:
a) If a^b = c , then log[base a] (c) = b and log of a on its own base is 1.
b) The two common bases are 10 and e.
c) log (d x f) = log(d) + log(f)
d) log (d/f) = log(d) - log(f)
f) log (d^f) = f log(d)

I believe those are all you need to know and the rest is practice, practice and practice.