In this example, we want to
compute log base 5 of 30,
rounded to three decimal places.
Since we can't compute log base
5 on our calculators directly,
but can compute the natural
log, which is the log base e,
we want to change the base using
a change of base formula, which
says log base b of x equals
log base a of x divided
by log base a of b.
So changing from base 5 to base
e, we get that log base 5 of 30
is the natural
log of 30, divided
by the natural log of 5.
And we can compute
the right hand side
with a calculator using
the natural log button.
Doing this we get that log
of 30 divided by a log of 5
comes to roughly 2.113.
So we can conclude that log
base 5 of 30 is roughly 2.113.
It's worth pointing
out here that we
could have changed the
base to either 10 or e,
but simply had to
pick one of them.
