SOLUTION: express {{{2 log ( x ) + 3 log ( y ) - log ( 7 )}}} as a single logarithm. I looked in my notes and got as far as : {{{ log ( x^2 )*( y^3 ) }}} but i don't know what to do wit

Question 236615: express as a single logarithm.
I looked in my notes and got as far as :
but i don't know what to do with the and i am not sure if what i have so far is right because in the notes it says be careful because has a different domain than . please help.
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2 log ( x ) + 3 log ( y ) - log ( 7 )
=============
= log(x^2) + log(y^3) - log(7)
---
= log[x^2*y^3/7]
======================
Cheers,
Stan H.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

You got as far as:

which is correct. Now we just use the "other" property of logarithms:

to combine the remaining two logarithms giving:

The original expression required that both x and y be positive numbers. This is still true for the combined, single logarithm (even though it may appear that x could be a negative because it is squared).
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