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:

log_{b}x + log_{b}y = log_{b}(xy)

You can check this by example:

log_{2}4 = 2 (because 2^{2}= 4) log_{2}8 = 3 (because 2^{3}= 8) log_{2}4 + log_{2}8 = 2 + 3 = 5 log_{2}(4 x 8) = log_{2}32 = 5 (because 2^{5}= 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.

log_{b}x - log_{b}y = log_{b}(x/y) a.log_{b}x = log_{b}(x^{a})

There are two special logs. In the same way that x^{0} = 1 and x^{1} = x we have:

log_{b}1 = 0 log_{b}b = 1

And finally, remember that log is the inverse of power. You can think of log and power as cancelling each other out. So:

log_{b}(b^{x}) = x b^{(logbx)}= x

Finally, not really a rule but a useful trick for turning numbers into logs:

x = x.1 = x.log_{b}b = log_{b}b^{x}

For example:

6 = 6log_{b}b = log_{b}b^{6}

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.