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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

Question 236615: express 2+log+%28+x+%29+%2B+3+log+%28+y+%29+-+log+%28+7+%29 as a single logarithm.
I looked in my notes and got as far as :
+log+%28+x%5E2+%29%2A%28+y%5E3+%29+ but i don't know what to do with the log+%287%29 and i am not sure if what i have so far is right because in the notes it says be careful because 2log+%28x%29 has a different domain than log+%28x%5E2%29. please help.
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
2+log+%28+x+%29+%2B+3+log+%28+y+%29+-+log+%28+7+%29
You got as far as:
log%28%28x%5E2%2Ay%5E3%29%29+-+log%28%287%29%29
which is correct. Now we just use the "other" property of logarithms:
log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29
to combine the remaining two logarithms giving:
log%28%28x%5E2%2Ay%5E3%2F7%29%29

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).