SOLUTION: log(5x) = log3+log(x-2) ...Just like that; no bases. PLEASE HELP!! -If you can go step by step with explanations that would be sooo helpful. Thank you!!

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Question 925847: log(5x) = log3+log(x-2) ...Just like that; no bases. PLEASE HELP!! -If you can go step by step with explanations that would be sooo helpful. Thank you!!
Found 3 solutions by lwsshak3, josmiceli, Edwin McCravy:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
log(5x) = log3+log(x-2)
when no base is shown, the base=10.



5x=3x-6
2x=-6
x=-3
no solution: x>0
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
When the base is not shown, the base is
normally , because there has to
be some base
----------------

use the following general rule on the right side:


-----------------------------
The next step can be stated as:
If the logs of 2 expressions are
equal, then the result of raising
the bases to those logs are equal, so
---------------------------------




------------------
check the answer:




-------------------
There is a problem with this, and you should get
more opinions on it. You can't possible get a
negative result by raising ( or any (+) base )
to any log. This seems to be what is happening.
What's the deep explanation, or is this a bogus
problem? Try to get an answer.



Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


The base is 10 anytime the base is not written.
But actually it doesn't matter what the base is.
We just need to know some rules of logaritms

Rule 1:   

Rule 2:  If  then we can drop the logs and write 

Start with 



We use rule 1 on the right side:



Now use rule 2



That's an easy equation to solve.  You should get -3

Trouble is, you must always check your answer to see if it
is an actual solution or just an extraneous answer.






Oh oh!  -3 is an extraneous answer because there is no such
number in real number mathematics as the logarithm of a negative
number.  Since when we checked we got a logarithm of a negative
number, we knew that the answer we got was extraneous and not a
real solution.

THERE IS NO SOLUTION!

Edwin
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