Question 174244: Please help! I've been show the rules, but I don't know how to apply them, could you please show me how?
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)
c. log3Y + log3Z (base 3)
d. log5Y - log5Z (base 5)
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384)   (Show Source):
Answer by josmiceli(19441)  (Show Source):
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 
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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.
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