You can
put this solution on YOUR website!3. Simplify the following expressions:
a. X4 * X5 (4 & 5 are exponents, I don't know how to type that)
=
=
.
b. Z9/Z10 (9 & 10 are exponents, I don't know how to type that)
=
=
OR
=
.
c. log3Y + log3Z (base 3)
=
=
.
d. log5Y - log5Z (base 5)
=
.
To review log rules see:
http://www.purplemath.com/modules/logrules.htm
You can
put this solution on YOUR website!Think of the problem as if there were no exponents involved
(a)
so,
This is
multiplied by itself
times, so
Aha! You just add the exponents
You can do any problem this way & discover the rule
(b)
There's 1 more
in the denominator, I'm left with
and I know
Aha!, I just do
---------------------
As for logs, just do a very simple experiment
How about
Big fact: ***** Logs are exponents!!! *****
So I'm adding 2 exponents here
The 1st term says: The exponent to the base
that gives me
The 2nd term says: The exponent to the base
that gives me
In the 1st case it's
because
In the 2nd case it's
because
So, now I,ve got
Remember that
is the sum of 2 logs, so it's a log.
Express it as log(2,?) or "log to the base
that gives me what?
If I raise
, so
A better way to write this is:
Aha! Add the exponents
These can be brain-twisters, and it helps if you've
wrestled aligators, but there's no easy way out.
