OK, let's evaluate each of
these three expressions using
our understanding of, well,
logarithms and the cancellation
properties.
So put a first.
Literally, this is the
cancellation property
written down immediately.
It's equal to 8--
instant.
If you wanted to see this
in several other ways,
log to the base 2
of 8 is 3, because 8
is 2 is the power of 3.
So you're taking
to the power of 3.
It's just 8 again.
OK, b, this one
doesn't quite match up.
It's close, but that 4
isn't so good, right?
So log to the base
2 of 4 to the 2.
So the issue basically is to
invoke a cancellation property.
That and the base
have to be identical.
Then it would just be
the exponent, of course,
by definition.
Doesn't quite work.
But remember, 4 was equal
to 2 to the power 2.
So this is log to the
base 2 of 2 squared,
which is equal to [INAUDIBLE]
laws of exponents.
Log to the base 2 of 2
times 2 is 2 to the 4.
Now, the cancellation property,
this is just equal to 4.
OK, c, this one is a
little bit trickier.
You gotta be really careful.
So the exponent, first of
all, so this is 3 to the power
log base 2 of 2 to the 3.
And thankfully, that
2 and that 2 match.
So that means I've got
an immediate cancellation
in the top.
So this is 3 now
to the power of 3.
That's equal to what?
It's equal to 27.
So just to label where the
cancellation properties
kick in--
cancellation property here,
and cancellation property
here, and of course cancellation
property used immediately here.
So this kind of
algebra with exponents
is very important,
not necessarily
for numerical values
like this, but when
you've got more
complicated expressions.
