Now that you know what logs are I’ll talk about how to use them. There are a few simple rules of logarithms that you’ll use to answer almost any log question. Each log rule is equivalent to a power rule, but if you get confused it might help to remember why we use logs: to turn multiplication into addition.
The Rules of Logs
If you remember your power rules, when you multiply the numbers you add the powers. So logs is the opposite: you multiply numbers by adding logs:
logbx + logby = logb(xy)
You can check this by example:
log24 = 2 (because 22 = 4) log28 = 3 (because 23 = 8) log24 + log28 = 2 + 3 = 5 log2(4 x 8) = log232 = 5 (because 25 = 32)
Note that – like all log rules – this only works if the base (b) is the same for both logs.
Here are the other log rules. I won’t give examples, you can easily make up your own if you want to try.
logbx - logby = logb(x/y) a.logbx = logb(xa)
There are two special logs. In the same way that x0 = 1 and x1 = x we have:
logb1 = 0 logbb = 1
And finally, remember that log is the inverse of power. You can think of log and power as cancelling each other out. So:
logb(bx) = x b(logbx) = x
Finally, not really a rule but a useful trick for turning numbers into logs:
x = x.1 = x.logbb = logbbx
For example:
6 = 6logbb = logbb6
With those few rules you should be able to answer any log question. In the next post I’ll show you my method for solving log questions.