How do you solve logs?

Answer 1

First you need to understand what a logarithm is. If y = bx, then x = logb(y), where b is the base of the logarithm. Typically, if the base is not given, like log(100), then the assumption is that the base is ten, so in the example of log(100), the answer is 2, since 102 = 100. The natural logarithm loge, is abbreviated ln(), and is programmed into many calculators and computer software.

That would obviously depend on the problem, but sometimes you can solve equations involving logarithms by taking antilogs on both sides. Also, quite often you need to apply the following basic properties of logarithms:

log(ab) = log a + log b

log(a/b) = log a - log b

log(ab) = b log a

And then, since many calculators and software have log (base 10) and natural log built in, but not other bases, this is helpful: logb(a) = log10(a)/log10(b)

or logb(a) = ln(a)/ln(b). So if you wanted to take the log (base 2) of a number (say 256 for example), you can do:log2(256) = ln(256)/ln(2) = 8.